Question

solve the system by substitution.
$8y + 3 = x$
$9x - 5y = -40$
answer attempt 1 out of 2
(\boxed{ }, \boxed{ }) submit answer

Explanation:

Step1: Substitute \( x = 8y + 3 \) into the second equation

We have the second equation \( 9x - 5y = -40 \). Substitute \( x \) with \( 8y + 3 \), so we get \( 9(8y + 3) - 5y = -40 \).

Step2: Simplify the left - hand side of the equation

First, expand \( 9(8y + 3) \) using the distributive property \( a(b + c)=ab+ac \). We have \( 9\times8y+9\times3-5y=-40 \), which simplifies to \( 72y + 27-5y=-40 \). Then combine like terms: \( (72y - 5y)+27=-40 \), so \( 67y+27 = - 40 \).

Step3: Solve for \( y \)

Subtract 27 from both sides of the equation: \( 67y+27 - 27=-40 - 27 \), which gives \( 67y=-67 \). Then divide both sides by 67: \( y=\frac{-67}{67}=-1 \).

Step4: Solve for \( x \)

Substitute \( y = - 1 \) into the first equation \( x = 8y+3 \). So \( x=8\times(-1)+3=-8 + 3=-5 \).

Answer:

\((-5,-1)\)