Questions: Solve the system by substitution. x = -y 8x + 3y = 40

Transcript text: Solve the system by substitution. \[ \begin{aligned} x & =-y \\ 8 x+3 y & =40 \end{aligned} \]

Solution

Solution Steps

To solve the system of equations by substitution, we first use the expression for \( x \) from the first equation, \( x = -y \), and substitute it into the second equation. This will allow us to solve for \( y \). Once we have the value of \( y \), we can substitute it back into the first equation to find the value of \( x \).

Step 1: Substitute \( x = -y \) into the Second Equation

Given the system of equations: \[ \begin{aligned} x & = -y \\ 8x + 3y & = 40 \end{aligned} \]

Substitute \( x = -y \) into the second equation: \[ 8(-y) + 3y = 40 \]

Step 2: Simplify and Solve for \( y \)

Simplify the equation: \[ -8y + 3y = 40 \]

Combine like terms: \[ -5y = 40 \]

Solve for \( y \): \[ y = -\frac{40}{5} = -8 \]

Step 3: Substitute \( y = -8 \) into the First Equation

Substitute \( y = -8 \) back into the first equation: \[ x = -(-8) \]

Simplify to find \( x \): \[ x = 8 \]