Question

for questions 12 and 13, determine the best method to solve the system of equations.
a substitution
b elimination using addition
c elimination using subtraction
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

Explanation:

Step1: Analyze the coefficients of \(y\) in question 12

In the system \(

$$\begin{cases}5x - 2y=4\\2x + 2y=8\end{cases}$$

\), the coefficients of \(y\) are \(- 2\) and \(2\). When we add the two equations \((5x-2y)+(2x + 2y)=4 + 8\), the \(y\) - terms will be eliminated.

Step2: Analyze the form of the equations in question 13

In the system \(

$$\begin{cases}y=3x + 12\\2x+y=16\end{cases}$$

\), the first equation is already solved for \(y\). We can substitute \(y = 3x+12\) into the second equation \(2x+(3x + 12)=16\).

Answer:

1. B. elimination using addition
2. A. substitution