Question

solve the system by substitution.

$y = -7x + 10$

$3x + 2y = 9$

Explanation:

Step1: Substitute \( y = -7x + 10 \) into \( 3x + 2y = 9 \)

We replace \( y \) in the second equation with the expression from the first equation. So we get \( 3x + 2(-7x + 10)=9 \).

Step2: Simplify the equation

First, distribute the 2: \( 3x-14x + 20 = 9 \). Then combine like terms: \( -11x+20 = 9 \).

Step3: Solve for \( x \)

Subtract 20 from both sides: \( -11x=9 - 20=-11 \). Then divide both sides by - 11: \( x=\frac{-11}{-11}=1 \).

Step4: Solve for \( y \)

Substitute \( x = 1 \) into \( y=-7x + 10 \). So \( y=-7(1)+10=-7 + 10 = 3 \).

Answer:

The solution to the system is \( x = 1 \), \( y = 3 \) (or as an ordered pair \( (1,3) \))