Question 1

Write the word or phrase that best completes each statement or answers the question.
-When graphing a linear inequality, the origin can always be used as a test point for determining which side of a boundary line should be shaded.

Accepted Answer

The origin (0,0) can be used as a test point unless the boundary line passes through the origin, in which case a different point must be chosen to determine the correct shading area.

Question 2

Write the word or phrase that best completes each statement or answers the question.
-x + y = -4 x + y = -5
A) (0, -9)
B) (-4  -5)
C) (0, 0)
D) $\text { Inconsistent, } \varnothing$

Accepted Answer

The two equations are contradictory since they have different constant terms. Therefore, there is no solution and the system is inconsistent. The answer is D.

Question 3

Write the word or phrase that best completes each statement or answers the question.
-Under what condition(s) will a system of two linear inequalities have no solution?

Accepted Answer

The answer of Write the word or phrase that best...

Question 4

Write the word or phrase that best completes each statement or answers the question.
-A system of two linear inequalities can have solutions in all quadrants.

Accepted Answer

Linear inequalities can have solutions in all four quadrants of the coordinate plane.

Question 5

Write the word or phrase that best completes each statement or answers the question.
-x - 5y = -4 x + 8y = -4
A) (0, -4)
B) (-4, 0)
C) (0, 4)
D) (4, 0)

Accepted Answer

The answer of Write the word or phrase that best...

Question 6

Write the word or phrase that best completes each statement or answers the question.
-Every system of two linear inequalities has infinitely many solutions.

Accepted Answer

Some systems of two linear inequalities may have no solution, especially if the inequalities represent parallel lines that do not overlap in their inequalities, or if they represent lines that form a region that does not intersect.

Question 7

Write the word or phrase that best completes each statement or answers the question.
-5x + 3y = 80 2x + y = 30
A) (10, 0)
B) (0, 0)
C) (0, 10)
D) (10, 10)

Accepted Answer

To solve the system of equations, we can use substitution or elimination. Using elimination, we can multiply the second equation by -3 and add it to the first equation to eliminate y:

5x + 3y = 80 
-6x - 3y = -90 
---------------- 
-x = -10

Solving for x, we get x = 10. Substituting back into the second equation, we can solve for y:

2x + y = 30 
2(10) + y = 30 
y = 10

Therefore, the solution is (10, 10). Choice letter D is the only option that represents (10, 10).

Question 8

Write the word or phrase that best completes each statement or answers the question.
-5x - 2y = -1 x + 4y = 35
A) (3, 8)
B) (2, 9)
C) (3, 9)
D) (2, 8)

Accepted Answer

To solve the system of equations, we can use either substitution or elimination. Here, elimination seems straightforward. Multiply the second equation by 5 to align the x coefficients:1) $5x - 2y = -1$2) $5(x + 4y) = 5(35)$This gives us:1) $5x - 2y = -1$2) $5x + 20y = 175$Subtracting the first equation from the second eliminates x, allowing us to solve for y. However, it seems there was a mistake in my calculation process, as directly solving the given system through substitution or elimination is more accurate:Using substitution, solve the second equation for x:$x = 35 - 4y$Substitute $x = 35 - 4y$ into the first equation:$5(35 - 4y) - 2y = -1$$175 - 20y - 2y = -1$$175 - 22y = -1$$-22y = -176$$y = 8$Substitute $y = 8$ into $x = 35 - 4y$:$x = 35 - 4(8)$$x = 35 - 32$$x = 3$Therefore, the solution is $x = 3$, $y = 8$, which corresponds to choice A) (3, 8).

Question 9

Solve the problem.
-In a recent school board election, the two candidates for president received 3064 votes. The loser received 608 fewer votes than the winner. How many votes did the winner receive?
A) 1836 votes
B) 1222 votes
C) 2456 votes
D) 1228 votes

Accepted Answer

Let the number of votes the winner received be x. Then the loser received x - 608 votes. The total votes are x + (x - 608) = 3064. Solving for x gives 2x - 608 = 3064, so 2x = 3672, and x = 1836. Thus, the winner received 1836 votes.

Question 10

Write the word or phrase that best completes each statement or answers the question.
-$$\begin{array} { l } 
x + y = 4 \
7 x + 7 y = 28
\end{array}$$
A) $( 0,0 )$
B) $( 2,2 )$
C) Dependent, $( x , - x + 4 )$
D) Inconsistent, $\varnothing$

Accepted Answer

The second equation is a multiple of the first, indicating the system has infinitely many solutions, making it dependent.

Question 11

Write the word or phrase that best completes each statement or answers the question.
-A system of two linear inequalities can have solutions in only one quadrant.

Accepted Answer

If both the inequalities in the system involve only one quadrant, then the solution will also lie in that quadrant only, hence making the statement true.

Question 12

Write the word or phrase that best completes each statement or answers the question.
-It is impossible for a system of two linear inequalities to have exactly one solution.

Accepted Answer

If there is exactly one solution, it means that the two inequalities intersect at a single point. However, this is not possible for linear inequalities, which define half-planes or lines. They can intersect at a line or along an entire plane, but not at a single point.

Question 13

Write the word or phrase that best completes each statement or answers the question.
-$$\begin{array} { l } 
5 x - 3 = y \
y - 5 x = 4
\end{array}$$
A) $( 0,0 )$
B) $( 5,3 )$
C) Dependent, $( x , 5 x - 3 )$
D) Inconsistent, $\varnothing$

Accepted Answer

The two equations represent parallel lines with the same slope but different y-intercepts, meaning they will never intersect. This makes the system inconsistent with no solution.

Question 14

Solve the problem.
-$$\text { Ioe has a collection of nickels and dimes that is worth }$$
A) 11 dimes
B) 8 dimes
C) 34 dimes
D) 23 dimes

Accepted Answer

The answer of Solve the problem.
-\[\text { Ioe has a...

Question 15

Solve the problem.
-There were 550 people at a play. The admission price was $2 for adults and $1 for children. The admission receipts were $830. How many adults and how many children attended?
A) 207 adults and 343 children
B) 270 adults and 280 children
C) 135 adults and 415 children
D) 280 adults and 270 children

Accepted Answer

The system of equations to solve this problem is: $A + C = 550$ (where A is the number of adults and C is the number of children) and $2A + C = 830$ (representing the total cost). Solving these equations simultaneously, we find that there were 280 adults and 270 children.

Question 16

Write the word or phrase that best completes each statement or answers the question.
-$$\begin{array} { l } 
x + 3 y = 3 \
2 x = - 6 y + 6
\end{array}$$
A) $( 3,3 )$
B) Dependent, $( x , - 3 x + 3 )$
C) Dependent, $\left( x , - \frac { 1 } { 3 } x + \frac { 3 } { 3 } \right)$
D) Inconsistent, $\varnothing$

Accepted Answer

We can solve the system of equations by eliminating the x variable:
\begin{align*}
x + 3y &= 3 \
2x &= -6y + 6 \
\end{align*}
Multiply the first equation by 2 to get:
\begin{align*}
2x + 6y &= 6 \
2x &= -6y + 6 \
\end{align*}
Add the two equations to eliminate x:
\begin{align*}
2x + 6y &= 6 \
+2x - 6y &= 6 \
\end{align*}
This simplifies to:
\begin{align*}
4x &= 12 \
x &= 3 \
\end{align*}
Substitute x=3 into one of the original equations to solve for y:
\begin{align*}
3 + 3y &= 3 \
3y &= 0 \
y &= 0 \
\end{align*}
Therefore, the solution to the system of equations is (3,0). However, if we write this solution in the form of a line, we can see that it is dependent on the value of x:
\begin{align*}
x + 3y &= 3 \
3y &= -x + 3 \
y &= -\frac{1}{3}x + 1 \
\end{align*}
This means that any point on the line y = -1/3x + 1 is a solution to the system of equations. Hence, the system is dependent and has infinitely many solutions, which can be expressed as (x, -1/3x + 1). Therefore, the best choice is C.

Question 17

Write the word or phrase that best completes each statement or answers the question.
-A system of two linear inequalities can have solutions in exactly three of the quadrants.

Accepted Answer

Since a system of two linear inequalities creates a shaded region on a coordinate plane, it is possible for the shaded region to cover exactly three of the four quadrants if the system is constructed to have a boundary line that passes through the origin.

Question 18

Write the word or phrase that best completes each statement or answers the question.
-x + 7y = -2 3x + y = 34
A) (7, 12)
B) (-2, 3)
C) (3, 7)
D) (12, -2)

Accepted Answer

To solve the system of equations, we can use either substitution or elimination. Using elimination, we can multiply the second equation by 7 to make the coefficients of y equal:x + 7y = -2(3x + y = 34) * 7 => 21x + 7y = 238Now, subtract the first equation from the modified second equation:21x + 7y - (x + 7y) = 238 - (-2)20x = 240x = 12Substitute x = 12 into one of the original equations to find y:12 + 7y = -27y = -14y = -2Therefore, the solution is (12, -2).

Question 19

Solve the problem.
-Devon purchased tickets to an air show for 5 adults and 2 children. The total cost was $112. The cost of a childʹs ticket was $7 less than the cost of an adultʹs ticket. Find the price of an adultʹs ticket
And a childʹs ticket.
A) adultʹs ticket: $20; childʹs ticket: $13
B) adultʹs ticket: $18; childʹs ticket: $11
C) adultʹs ticket: $19; childʹs ticket: $12
D) adultʹs ticket: $17; childʹs ticket: $10

Accepted Answer

The answer of Solve the problem.
-Devon purchased tickets to an...

Question 20

Write the word or phrase that best completes each statement or answers the question.
-When graphing a system of two linear inequalities, the final shaded region is made up of all points which belong to the graphs of either of the individual inequalities.

Accepted Answer

The final shaded region is made up of all points that satisfy both of the individual inequalities, not just one or the other.

Quiz 4: Systems of Equations

Write the word or phrase that best completes each statement or answers the question. -When graphing a linear inequality, the origin can always be used as a test point for determining which side of a boundary line should be shaded.

Write the word or phrase that best completes each statement or answers the question. -x + y = -4 x + y = -5

Write the word or phrase that best completes each statement or answers the question. -Under what condition(s) will a system of two linear inequalities have no solution?

Write the word or phrase that best completes each statement or answers the question. -A system of two linear inequalities can have solutions in all quadrants.

Write the word or phrase that best completes each statement or answers the question. -x - 5y = -4 x + 8y = -4

Write the word or phrase that best completes each statement or answers the question. -Every system of two linear inequalities has infinitely many solutions.

Write the word or phrase that best completes each statement or answers the question. -5x + 3y = 80 2x + y = 30

Write the word or phrase that best completes each statement or answers the question. -5x - 2y = -1 x + 4y = 35

Solve the problem. -In a recent school board election, the two candidates for president received 3064 votes. The loser received 608 fewer votes than the winner. How many votes did the winner receive?

Write the word or phrase that best completes each statement or answers the question. - $\begin{array} { l } x + y = 4 \\7 x + 7 y = 28\end{array}$

Write the word or phrase that best completes each statement or answers the question. -A system of two linear inequalities can have solutions in only one quadrant.

Write the word or phrase that best completes each statement or answers the question. -It is impossible for a system of two linear inequalities to have exactly one solution.

Write the word or phrase that best completes each statement or answers the question. - $\begin{array} { l } 5 x - 3 = y \\y - 5 x = 4\end{array}$

Solve the problem. - $\text { Ioe has a collection of nickels and dimes that is worth }$

Solve the problem. -There were 550 people at a play. The admission price was $2 for adults and $1 for children. The admission receipts were $830. How many adults and how many children attended?

Write the word or phrase that best completes each statement or answers the question. - $\begin{array} { l } x + 3 y = 3 \\2 x = - 6 y + 6\end{array}$

Write the word or phrase that best completes each statement or answers the question. -A system of two linear inequalities can have solutions in exactly three of the quadrants.

Write the word or phrase that best completes each statement or answers the question. -x + 7y = -2 3x + y = 34

Solve the problem. -Devon purchased tickets to an air show for 5 adults and 2 children. The total cost was $112. The cost of a childʹs ticket was $7 less than the cost of an adultʹs ticket. Find the price of an adultʹs ticket And a childʹs ticket.

Write the word or phrase that best completes each statement or answers the question. -When graphing a system of two linear inequalities, the final shaded region is made up of all points which belong to the graphs of either of the individual inequalities.