Question

a substitution
c elimination using subtraction
b elimination using addition
d elimination using multiplication

1. $5x - 2y = 4$

$2x + 2y = 8$

1. $y = 3x + 12$

$2x + y = 16$

1. the length of a rectangle is three times the width. the sum of the length and the width is 24 inches. what is the length of the rectangle?

f 3 inches
g 6 inches
h 9 inches
j 18 inches

1. an airport shuttle company owns sedans that have a maximum capacity of 3 passengers and vans that have a maximum capacity of 8 passengers. their 12 vehicles have a combined maximum capacity of 61 passengers. how many vans does the company own?

a 5
b 8
c 12
d 7
for questions 16 and 17, use the graph.

1. what is a solution to the system of inequalities?

a $(0,2)$
b $(0,0)$
c $(1,1)$
d $(2,4)$

1. what system of inequalities is represented?

f $y < x + 2$
$y leq -x + 1$
g $y > x + 2$
$y leq -x + 1$
h $y > x + 2$
$y geq -x + 1$
j $y < x + 2$
$y geq -x + 1$
bonus determine the best method to solve the system of equations. then solve
$x - 3y = 0$
$2x - 7y = 0$

Explanation:

Step1: Substitute \(x = 3y\) into \(2x-7y = 0\)

From \(x - 3y=0\), we get \(x = 3y\). Substitute \(x = 3y\) into \(2x-7y = 0\), we have \(2(3y)-7y = 0\).

Step2: Simplify the equation

Expand \(2(3y)-7y = 0\) to \(6y-7y = 0\), then \(-y=0\), so \(y = 0\).

Step3: Find the value of \(x\)

Substitute \(y = 0\) into \(x = 3y\), we get \(x=3\times0 = 0\).

Answer:

\(x = 0,y = 0\)