Question

solve the system by substitution.
$7x - 9 = y$
$-5x + 7y = -19$

Explanation:

Step1: Substitute \( y = 7x - 9 \) into the second equation

We have the second equation \( -5x + 7y = -19 \). Replace \( y \) with \( 7x - 9 \), so we get \( -5x + 7(7x - 9) = -19 \).

Step2: Simplify and solve for \( x \)

First, expand the left - hand side: \( -5x+49x - 63=-19 \).
Combine like terms: \( 44x-63 = - 19 \).
Add 63 to both sides: \( 44x=-19 + 63=44 \).
Divide both sides by 44: \( x = 1 \).

Step3: Substitute \( x = 1 \) into \( y = 7x - 9 \) to find \( y \)

Substitute \( x = 1 \) into \( y = 7x-9 \), we have \( y=7\times1 - 9=7 - 9=-2 \).

Answer:

The solution of the system is \( x = 1,y=-2 \)