Question

solve the system by substitution.
$2x - 3y = 20$
$x = -2y + 3$

Explanation:

Step1: Substitute \( x = -2y + 3 \) into \( 2x - 3y = 20 \)

Substitute \( x \) in the first equation with \( -2y + 3 \), we get:
\( 2(-2y + 3) - 3y = 20 \)

Step2: Simplify the equation

First, distribute the 2:
\( -4y + 6 - 3y = 20 \)
Then, combine like terms:
\( -7y + 6 = 20 \)
Subtract 6 from both sides:
\( -7y = 20 - 6 \)
\( -7y = 14 \)

Step3: Solve for \( y \)

Divide both sides by -7:
\( y = \frac{14}{-7} \)
\( y = -2 \)

Step4: Substitute \( y = -2 \) back into \( x = -2y + 3 \)

\( x = -2(-2) + 3 \)
\( x = 4 + 3 \)
\( x = 7 \)

Answer:

The solution to the system is \( x = 7 \), \( y = -2 \)