Questions: Solve the system by substitution. -10x + 3y = 34 y = -8x

Solve the system by substitution. -10x + 3y = 34 y = -8x
Transcript text: Solve the system by substitution. \[ \begin{aligned} -10 x+3 y & =34 \\ y & =-8 x \end{aligned} \]
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Solution

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Solution Steps

To solve the system of equations by substitution, we can follow these steps:

  1. Substitute the expression for \( y \) from the second equation into the first equation.
  2. Solve the resulting equation for \( x \).
  3. Substitute the value of \( x \) back into the second equation to find \( y \).
Step 1: Substitute \( y \) in the First Equation

We start with the system of equations: \[ \begin{aligned} -10x + 3y &= 34 \quad (1) \\ y &= -8x \quad (2) \end{aligned} \] Substituting equation (2) into equation (1): \[ -10x + 3(-8x) = 34 \] This simplifies to: \[ -10x - 24x = 34 \] Combining like terms gives: \[ -34x = 34 \]

Step 2: Solve for \( x \)

To isolate \( x \), we divide both sides by -34: \[ x = -1 \]

Step 3: Find \( y \)

Now, we substitute \( x = -1 \) back into equation (2) to find \( y \): \[ y = -8(-1) = 8 \]

Final Answer

The solution to the system of equations is: \[ \boxed{x = -1} \quad \text{and} \quad \boxed{y = 8} \]

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