Question

1. use substitution to solve the following system of eq

-7x - 2y = -13
x - 2y = 11
x =

y =

check

Explanation:

Step1: Solve the second equation for x

From \( x - 2y = 11 \), we can express \( x \) in terms of \( y \) by adding \( 2y \) to both sides. So, \( x = 2y + 11 \).

Step2: Substitute x into the first equation

Substitute \( x = 2y + 11 \) into \( -7x - 2y = -13 \). We get:
\( -7(2y + 11) - 2y = -13 \)
First, distribute the -7: \( -14y - 77 - 2y = -13 \)
Combine like terms: \( -16y - 77 = -13 \)

Step3: Solve for y

Add 77 to both sides: \( -16y = -13 + 77 \)
\( -16y = 64 \)
Divide both sides by -16: \( y = \frac{64}{-16} = -4 \)

Step4: Substitute y back to find x

Now that we know \( y = -4 \), substitute it into \( x = 2y + 11 \).
\( x = 2(-4) + 11 \)
\( x = -8 + 11 = 3 \)

Answer:

\( x = 3 \)
\( y = -4 \)