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.
-2x - 3y = 9 6x - 9y = 36

Accepted Answer

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

2x - 3y = 9 
-3y = -2x + 9 
y = (2/3)x - 3

6x - 9y = 36 
-9y = -6x + 36 
y = (2/3)x - 4

We can see that these two equations have the same slope, but different y-intercepts. This means they are parallel lines, and therefore there is no solution. To convert the first equation into slope-intercept form, we need to solve for y:
2x - 3y = 9
-3y = -2x + 9
y = (2/3)x - 3

Similarly, to convert the second equation into slope-intercept form, we need to solve for y:
6x - 9y = 36
-9y = -6x + 36
y = (2/3)x - 4

Notice that both equations have the same slope of 2/3. However, their y-intercepts are different (one is -3 and the other is -4). Therefore, the two lines are parallel and will never intersect. This means that there is no solution to the system of equations. The answer is choice B.

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.
-x + y = -4 x + y = 8

Accepted Answer

To put both equations in slope-intercept form, we need to solve for y:
x + y = -4 
y = -x - 4

x + y = 8 
y = -x + 8

Now we can see that the slope of both lines is -1, meaning they are parallel. Parallel lines never intersect, so there is no solution to this system of equations. The answer is B, no solution. To get the equations into slope-intercept form, we need to solve for y.

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

x + y = 8
y = -x + 8

Now we can see that the two equations have different slopes (-1 and -1), meaning they are not parallel lines. However, they also have different y-intercepts (-4 and 8), meaning they do not intersect. Therefore, there is no solution to this system of equations.

Question 3

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.
-9x = 6y + 3 9x = 6y - 5

Accepted Answer

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

9x = 6y + 3 becomes y = (3/2)x + 1/2

9x = 6y - 5 becomes y = (3/2)x - 5/6

Now we can see that the slopes are equal (3/2) but the y-intercepts are different (1/2 vs -5/6). This means that the lines are parallel and will never intersect, so there is no solution. Therefore, the best choice is B. To write the equations in slope-intercept form, we need to solve for y:
9x = 6y + 3  -> 6y = 9x - 3  -> y = (9/6)x - 1/2
9x = 6y - 5 -> 6y = 9x + 5 -> y = (9/6)x + 5/6
Now we can see the slopes of the two lines are equal, but their y-intercepts are different. Therefore, the two lines are parallel and never intersect. Thus, the system of equations has no solution.

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.
-4x + 6y = 44 4x + 2y = 52

Accepted Answer

To express the equations in slope-intercept form (y = mx + b), we solve each for y:  1) 4x + 6y = 44 becomes y = -2/3x + 22/3  2) 4x + 2y = 52 becomes y = -2x + 26  The slopes are different (-2/3 and -2), indicating the lines are not parallel and will intersect at exactly one point, so there is 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.
-x + y = -50
Y = 9x

Accepted Answer

The first equation can be rewritten as y = -x - 50, and the second equation is already in slope-intercept form as y = 9x. Since the slopes of the two lines (-1 and 9) are different, the lines will intersect at exactly one point, indicating exactly one solution.

Question 6

Determine if the following ordered pair satisfies the system of linear equations.
-

Accepted Answer

The answer of Determine if the following ordered pair satisfies...

Question 7

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.
-6x - 4y = 2 -12x + 8y = -8

Accepted Answer

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

Question 8

Identify the system of linear equations as consistent, inconsistent, or dependent. State whether the system has exactly one
solution, no solution, or an infinite number of solutions.
-

Accepted Answer

The answer of Identify the system of linear equations as...

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.
-5x - 7y = -9 5x - 7y = 9

Accepted Answer

By rearranging the equations in slope-intercept form:
5x - 7y = -9 becomes y = (5/7)x + 9/7
5x - 7y = 9 becomes y = (5/7)x - 9/7
These equations have different y-intercepts, which means they have different lines. Therefore, the system of equations has no solution. First, let's rewrite each equation in slope-intercept form.

5x - 7y = -9  becomes y = (5/7)x + 9/7

5x - 7y = 9  becomes y = (5/7)x - 9/7

Notice that the slopes of the two equations are the same (5/7). This means that the two lines are parallel and will never intersect. Therefore, there are no solutions to the system of equations.

So the best choice is C, no solution.

Question 10

Identify the system of linear equations as consistent, inconsistent, or dependent. State whether the system has exactly one
solution, no solution, or an infinite number of solutions.
-

Accepted Answer

The system of equations has two identical equations. Therefore, it is dependent and has an infinite number of solutions. The system has two equations with the exact same coefficients, which means they are essentially the same equation. This makes the system dependent and has an infinite number of solutions.

Question 11

Identify the system of linear equations as consistent, inconsistent, or dependent. State whether the system has exactly one
solution, no solution, or an infinite number of solutions.
-

Accepted Answer

The answer of Identify the system of linear equations as...

Question 12

Determine if the following ordered pair satisfies the system of linear equations.
-(-6, -2) 4x + y = -22
3x + 4y = -10

Accepted Answer

Substituting x=-6 and y=-2 in the first equation, we get 4(-6) + (-2) = -22, which simplifies to -24 - 2 = -26, so the ordered pair (-6,-2) does not satisfy the first equation. Hence, it cannot satisfy the system of linear equations.

Question 13

Identify the system of linear equations as consistent, inconsistent, or dependent. State whether the system has exactly one
solution, no solution, or an infinite number of solutions.
-

Accepted Answer

The answer of Identify the system of linear equations as...

Question 14

Determine if the following ordered pair satisfies the system of linear equations.
-(6, 2) 2x = -10 - y
3x = -14 - 2y

Accepted Answer

If we substitute x=6 and y=2 into both equations, we get:
2(6) = -10 - (2)  --> 12 = -8 (which is not true)
3(6) = -14 - 2(2) --> 18 = -18 (which is also not true)
Therefore, (6,2) does not satisfy the system of linear equations. To check if (6,2) satisfies the system of linear equations, we need to substitute x=6 and y=2 in both equations and see if they are true.

For the first equation, 
2x = -10 - y 
2(6) = -10 -2 
12 = -12 
This is false.

For the second equation, 
3x = -14 - 2y 
3(6) = -14 -2(2) 
18 = -18 
This is also false.

Therefore, the ordered pair (6,2) does not satisfy the system of linear equations.

Question 15

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.
-x + y = -1 x - y = 11

Accepted Answer

The given equations are x + y = -1 and x - y = 11. To express them in slope-intercept form (y = mx + b), we solve each for y:1. x + y = -1 => y = -x - 12. x - y = 11 => y = x - 11These equations represent lines with different slopes, meaning they will intersect at exactly one point. Therefore, the system has one solution.

Question 16

Determine if the following ordered pair satisfies the system of linear equations.
-(-2, 6) y = 4x + 14
Y = -3x

Accepted Answer

(-2, 6) satisfies both equations.

Question 17

Determine if the following ordered pair satisfies the system of linear equations.
-

Accepted Answer

The answer of Determine if the following ordered pair satisfies...

Question 18

Determine if the following ordered pair satisfies the system of linear equations.
-(-4, -3) x + y = 1
X - y = 7

Accepted Answer

If we substitute x=-4 and y=-3 into both equations, we get:
-4 + (-3) = -7  not equal to 1
-4 - (-3) = -1 not equal to 7
Therefore, (-4, -3) does not satisfy the system of linear equations. First equation becomes
(-4) + (-3) = 1
-7 = 1 which is not true.
Thus (-4, -3) does not satisfy the system of linear equations.

Question 19

Identify the system of linear equations as consistent, inconsistent, or dependent. State whether the system has exactly one
solution, no solution, or an infinite number of solutions.
-

Accepted Answer

The answer of Identify the system of linear equations as...

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 = x - 6 x - 5y = 30

Accepted Answer

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

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. -2x - 3y = 9 6x - 9y = 36

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. -x + y = -4 x + y = 8

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. -9x = 6y + 3 9x = 6y - 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 + 6y = 44 4x + 2y = 52

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. -x + y = -50 Y = 9x

Determine if the following ordered pair satisfies the system 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. -6x - 4y = 2 -12x + 8y = -8

Identify the system of linear equations as consistent, inconsistent, or dependent. State whether the system 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. -5x - 7y = -9 5x - 7y = 9

Identify the system of linear equations as consistent, inconsistent, or dependent. State whether the system has exactly one solution, no solution, or an infinite number of solutions. -

Identify the system of linear equations as consistent, inconsistent, or dependent. State whether the system has exactly one solution, no solution, or an infinite number of solutions. -

Determine if the following ordered pair satisfies the system of linear equations. -(-6, -2) 4x + y = -22 3x + 4y = -10

Identify the system of linear equations as consistent, inconsistent, or dependent. State whether the system has exactly one solution, no solution, or an infinite number of solutions. -

Determine if the following ordered pair satisfies the system of linear equations. -(6, 2) 2x = -10 - y 3x = -14 - 2y

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. -x + y = -1 x - y = 11

Determine if the following ordered pair satisfies the system of linear equations. -(-2, 6) y = 4x + 14 Y = -3x

Determine if the following ordered pair satisfies the system of linear equations. -

Determine if the following ordered pair satisfies the system of linear equations. -(-4, -3) x + y = 1 X - y = 7

Identify the system of linear equations as consistent, inconsistent, or dependent. State whether the system 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 = x - 6 x - 5y = 30