Question 1

Express each equation in slope-intercept form. Without graphing the equations, state whether the system of equations
has exactly one solution, no solution, or an infinite number of solutions.
-
A) one solution
B) no solution
C) infinite number of solutions

Accepted Answer

Both equations can be rewritten in slope-intercept form: 
y = 2x + 5 
y = 2x - 3 
Since the slope is the same for both equations (2), this means that the lines are parallel and will never intersect. Therefore, there is no solution. However, since there is only one possible outcome, there is no need to choose multiple choices. The two equations are:

y = 2x + 1

y = -2x + 5

To convert these equations to slope-intercept form, we need to solve for y:

y = 2x + 1 becomes y = mx + b, where m is the slope and b is the y-intercept. In this case, m = 2 and b = 1, so the equation in slope-intercept form is:

y = 2x + 1

y = -2x + 5 also becomes y = mx + b, where m is the slope and b is the y-intercept. In this case, m = -2 and b = 5, so the equation in slope-intercept form is:

y = -2x + 5

Since these two equations have different slopes and y-intercepts, they intersect at exactly one point, so the system has one solution.

Question 2

Express each equation in slope-intercept form. Without graphing the equations, state whether the system of equations
has exactly one solution, no solution, or an infinite number of solutions.
-y - 4x = 5 5y = 20x + 25
A) one solution
B) no solution
C) infinite number of solutions

Accepted Answer

First, we need to convert both equations into slope-intercept form:

y - 4x = 5  =>  y = 4x + 5

5y = 20x + 25  =>  y = 4x + 5

Notice that both equations have the same slope-intercept form, which means they represent the same line. Therefore, there are infinitely many solutions to this system of equations. To write both equations in slope-intercept form, we need to solve for y.

y - 4x = 5 
y = 4x + 5

5y = 20x + 25 
y = 4x + 5

We can see that both equations have the same slope-intercept form: y = 4x + 5. This means that their graphs are identical and they represent the same line. Therefore, there are infinite solutions to the system of equations.

Question 3

Determine the solution to the system of linear equations graphically. If the system is dependent or inconsistent, so state.
-
A) (-1.5, -1)
B) (1, 1)
C) dependent
D) inconsistent

Accepted Answer

The answer of Determine the solution to the system of...

Question 4

Express each equation in slope-intercept form. Without graphing the equations, state whether the system of equations
has exactly one solution, no solution, or an infinite number of solutions.
-5x + y = 0 4x - 2y = -14
A) no solution
B) infinite number of solutions
C) one solution

Accepted Answer

To write the equations in slope-intercept form, we need to solve for y:

5x + y = 0  => y = -5x
4x - 2y = -14 => y = 2x + 7

Now we can see that the equations have different slopes (slope of -5 for the first equation and slope of 2 for the second equation) and different y-intercepts (0 for the first equation and 7 for the second equation). Therefore, they intersect at exactly one point, meaning there is one solution. First, let's convert both equations into slope-intercept form:

5x + y = 0 => y = -5x (slope = -5, y-intercept = 0)

4x - 2y = -14 => y = 2x + 7 (slope = 2, y-intercept = 7)

Now, we can see that the slopes of the two lines are different (-5 and 2), so the lines are not parallel. Therefore, they will intersect at exactly one point, which means there is one solution.

Therefore, the answer is C: one solution.

Question 5

Express each equation in slope-intercept form. Without graphing the equations, state whether the system of equations
has exactly one solution, no solution, or an infinite number of solutions.
-4x - 2y = -18 x = -4y
A) infinite number of solutions
B) one solution
C) no solution

Accepted Answer

To express the given equations in slope-intercept form (y = mx + b), we first solve each equation for y.1. For the first equation, 4x - 2y = -18, we solve for y:   -2y = -4x - 18   y = 2x + 92. For the second equation, x = -4y, we solve for y:   y = -1/4xNow, we have the two equations in slope-intercept form:y = 2x + 9 and y = -1/4x.Since the slopes of the two lines (2 and -1/4) are different, the lines are not parallel and will intersect at exactly one point. Therefore, the system of equations has exactly one solution.

Question 6

Determine the solution to the system of linear equations graphically. If the system is dependent or inconsistent, so state.
-
A) (2, 0)
B) 12 , 0
C) dependent
D) inconsistent

Accepted Answer

The answer of Determine the solution to the system of...

Question 7

Determine the solution to the system of linear equations graphically. If the system is dependent or inconsistent, so state.
-
A) (1, 1)
B) (1, 5)
C) dependent
D) inconsistent

Accepted Answer

The answer of Determine the solution to the system of...

Question 8

Determine the solution to the system of linear equations graphically. If the system is dependent or inconsistent, so state.
-
A) (1, -8)
B) (-1, 8)
C) (-1, -8)
D) (1, 16)

Accepted Answer

From the graph, the two lines intersect at the point (1, -8), which is the solution to the system of linear equations. Therefore, the answer is choice A.

Question 9

Express each equation in slope-intercept form. Without graphing the equations, state whether the system of equations
has exactly one solution, no solution, or an infinite number of solutions.
-
A) no solution
B) one solution
C) infinite number of solutions

Accepted Answer

Since both equations have the same slope but different y-intercepts, they are parallel lines and do not intersect. Therefore, there is no solution to the system of equations. The equations are not given in slope-intercept form, but we can rewrite them as y = 2x + 5 and y = 2x + 7. These equations have the same slope (2) but different y-intercepts (5 and 7). Therefore, the lines are parallel and never intersect, so there is no solution to the system of equations.

Question 10

Determine the solution to the system of linear equations graphically. If the system is dependent or inconsistent, so state.
-
A) (0, 12)
B) (5, -3)
C) dependent
D) inconsistent

Accepted Answer

The answer of Determine the solution to the system of...

Question 11

Determine the solution to the system of linear equations graphically. If the system is dependent or inconsistent, so state.
-
A) (3, 2)
B) (2, 3)
C) dependent
D) inconsistent

Accepted Answer

The answer of Determine the solution to the system of...

Question 12

Express each equation in slope-intercept form. Without graphing the equations, state whether the system of equations
has exactly one solution, no solution, or an infinite number of solutions.
-y = 3x - 1 5y + 20x = 65
A) no solution
B) one solution
C) infinite number of solutions

Accepted Answer

First, we need to convert the second equation into slope-intercept form:
5y + 20x = 65
5y = -20x + 65
y = -4x + 13

Now we have the two equations in slope-intercept form:
y = 3x - 1
y = -4x + 13

Since the slopes of the two lines are different (3 and -4), the system has one solution. If the slopes had been equal and the y-intercepts different, the system would have no solution, and if the slopes and y-intercepts had been equal, the system would have infinitely many solutions. But in this case, the lines intersect at exactly one point, so there is one solution. First, we need to write the second equation in slope-intercept form.

5y + 20x = 65

5y = -20x + 65

y = -4x + 13

Now we have two equations in slope-intercept form:

y = 3x - 1 
y = -4x + 13

We can see that these lines have different slopes, so they intersect at exactly one point. Therefore, the system of equations has one solution.

Question 13

Determine the solution to the system of linear equations graphically. If the system is dependent or inconsistent, so state.
-
A) (0,0)
B) (4, 5)
C) dependent
D) inconsistent

Accepted Answer

The answer of Determine the solution to the system of...

Question 14

Express each equation in slope-intercept form. Without graphing the equations, state whether the system of equations
has exactly one solution, no solution, or an infinite number of solutions.
--7y = x + 34 2x + 6y = -36
A) infinite number of solutions
B) no solution
C) one solution

Accepted Answer

To determine the number of solutions, we first express both equations in slope-intercept form (y = mx + b). For the first equation, -7y = x + 34, we divide by -7 to get y = -1/7x - 34/7. For the second equation, 2x + 6y = -36, we rearrange it to get 6y = -2x - 36 and then divide by 6 to get y = -1/3x - 6. Since the slopes (-1/7 and -1/3) are different, the lines will intersect at exactly one point, indicating one solution.

Question 15

Determine the solution to the system of linear equations graphically. If the system is dependent or inconsistent, so state.
-
A) (0, 0)
B) (1, 0)
C) (1, 1)
D) (0, 1)

Accepted Answer

The answer of Determine the solution to the system of...

Question 16

Express each equation in slope-intercept form. Without graphing the equations, state whether the system of equations
has exactly one solution, no solution, or an infinite number of solutions.
-
A) no solution
B) one solution
C) infinite number of solutions

Accepted Answer

The answer of Express each equation in slope-intercept form. Without...

Question 17

Express each equation in slope-intercept form. Without graphing the equations, state whether the system of equations
has exactly one solution, no solution, or an infinite number of solutions.
-2y = x + 24 2x + 4y = 0
A) no solution
B) one solution
C) infinite number of solutions

Accepted Answer

To express each equation in slope-intercept form (y = mx + b), we first solve each equation for y.1. For the first equation, 2y = x + 24, divide everything by 2 to isolate y:$$y = \frac{1}{2}x + 12$$2. For the second equation, 2x + 4y = 0, first isolate 4y:$$4y = -2x$$Then, divide everything by 4 to solve for y:$$y = -\frac{1}{2}x$$Now, we have the two equations in slope-intercept form:$$y = \frac{1}{2}x + 12$$$$y = -\frac{1}{2}x$$These two lines have different slopes, which means they will intersect at exactly one point. Therefore, the system of equations has exactly one solution.

Question 18

Express each equation in slope-intercept form. Without graphing the equations, state whether the system of equations
has exactly one solution, no solution, or an infinite number of solutions.
-2x + y = 8 8x + 4y = 32
A) one solution
B) no solution
C) infinite number of solutions

Accepted Answer

To write the equations in slope-intercept form, we need to solve for y in each equation:

2x + y = 8
y = -2x + 8

8x + 4y = 32
4y = -8x + 32
y = -2x + 8

As we can see, the two equations have the exact same slope-intercept form, meaning they represent the same line. Therefore, there are an infinite number of solutions to this system of equations. First, we need to express both equations in slope-intercept form, which means solving for y:
2x + y = 8 
y = -2x + 8

8x + 4y = 32 
4y = -8x + 32 
y = -2x + 8

As we can see, both equations have the same slope (-2) and y-intercept (8), which means they represent the same line. Therefore, there are infinitely many solutions to this system of equations, and the answer is C.

Question 19

Express each equation in slope-intercept form. Without graphing the equations, state whether the system of equations
has exactly one solution, no solution, or an infinite number of solutions.
--3x - 9y = -10 5x + 15y = 0
A) one solution
B) infinite number of solutions
C) no solution

Accepted Answer

We can rewrite the first equation as -9y = 3x - 10, or y = (-1/3)x + (10/9). Similarly, we can rewrite the second equation as 15y = -5x, or y = (-1/3)x. Since the slopes are the same (-1/3), but the y-intercepts are different, the system has no solution. First, we need to rewrite both equations in slope-intercept form.
-3x - 9y = -10
-3x + 10 = 9y
(-3/9)x + 10/9 = y
y = (-1/3)x + 10/9
5x + 15y = 0
5x = -15y
x = -3y
y = (-1/3)x
As we can see, the two equations have the same slope (-1/3), but different y-intercepts (10/9 and 0). Therefore, the system of equations represents two parallel lines that do not intersect and have no solution. The correct choice is C.

Question 20

Express each equation in slope-intercept form. Without graphing the equations, state whether the system of equations
has exactly one solution, no solution, or an infinite number of solutions.
-y y == 47x x -- 2 3
A) infinite number of solutions
B) one solution
C) no solution

Accepted Answer

To write the equation in slope-intercept form:

y = 47x - 2/3

Since the equation is in slope-intercept form, there is only one solution.

Quiz 9: Systems of Linear Equations

Express each equation in slope-intercept form. Without graphing the equations, state whether the system of equations has exactly one solution, no solution, or an infinite number of solutions. -

Express each equation in slope-intercept form. Without graphing the equations, state whether the system of equations has exactly one solution, no solution, or an infinite number of solutions. -y - 4x = 5 5y = 20x + 25

Determine the solution to the system of linear equations graphically. If the system is dependent or inconsistent, so state. -

Express each equation in slope-intercept form. Without graphing the equations, state whether the system of equations has exactly one solution, no solution, or an infinite number of solutions. -5x + y = 0 4x - 2y = -14

Express each equation in slope-intercept form. Without graphing the equations, state whether the system of equations has exactly one solution, no solution, or an infinite number of solutions. -4x - 2y = -18 x = -4y

Determine the solution to the system of linear equations graphically. If the system is dependent or inconsistent, so state. -

Determine the solution to the system of linear equations graphically. If the system is dependent or inconsistent, so state. -

Determine the solution to the system of linear equations graphically. If the system is dependent or inconsistent, so state. -

Express each equation in slope-intercept form. Without graphing the equations, state whether the system of equations has exactly one solution, no solution, or an infinite number of solutions. -

Determine the solution to the system of linear equations graphically. If the system is dependent or inconsistent, so state. -

Determine the solution to the system of linear equations graphically. If the system is dependent or inconsistent, so state. -

Express each equation in slope-intercept form. Without graphing the equations, state whether the system of equations has exactly one solution, no solution, or an infinite number of solutions. -y = 3x - 1 5y + 20x = 65

Determine the solution to the system of linear equations graphically. If the system is dependent or inconsistent, so state. -

Express each equation in slope-intercept form. Without graphing the equations, state whether the system of equations has exactly one solution, no solution, or an infinite number of solutions. --7y = x + 34 2x + 6y = -36

Determine the solution to the system of linear equations graphically. If the system is dependent or inconsistent, so state. -

Express each equation in slope-intercept form. Without graphing the equations, state whether the system of equations has exactly one solution, no solution, or an infinite number of solutions. -

Express each equation in slope-intercept form. Without graphing the equations, state whether the system of equations has exactly one solution, no solution, or an infinite number of solutions. -2y = x + 24 2x + 4y = 0

Express each equation in slope-intercept form. Without graphing the equations, state whether the system of equations has exactly one solution, no solution, or an infinite number of solutions. -2x + y = 8 8x + 4y = 32

Express each equation in slope-intercept form. Without graphing the equations, state whether the system of equations has exactly one solution, no solution, or an infinite number of solutions. --3x - 9y = -10 5x + 15y = 0

Express each equation in slope-intercept form. Without graphing the equations, state whether the system of equations has exactly one solution, no solution, or an infinite number of solutions. -y y == 47x x -- 2 3