Question

solve the system by substitution.
$5x + 2y = 17$
$-4x + 7 = y$

Explanation:

Step1: Substitute \( y = -4x + 7 \) into the first equation

We have the first equation \( 5x + 2y = 17 \). Replace \( y \) with \( -4x + 7 \), so we get \( 5x + 2(-4x + 7) = 17 \).

Step2: Simplify and solve for \( x \)

First, expand the left - hand side: \( 5x-8x + 14 = 17 \).
Combine like terms: \( -3x+14 = 17 \).
Subtract 14 from both sides: \( -3x=17 - 14=3 \).
Divide both sides by - 3: \( x=\frac{3}{-3}=-1 \).

Step3: Substitute \( x = - 1 \) into the equation for \( y \)

We know that \( y=-4x + 7 \). Substitute \( x=-1 \) into this equation: \( y=-4\times(-1)+7 \).
Calculate the value of \( y \): \( y = 4 + 7=11 \).

Answer:

The solution of the system is \( x=-1,y = 11 \)