Question
Solve the system by substitution. \[ \begin{aligned} y & =-4 x \\ y & =-5 x+5\end{aligned} \]
Ask by John Beck. in the United States
Feb 03,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
\( x = 5 \) and \( y = -20 \).
Solution
To solve the given system of equations by substitution:
\[
\begin{aligned}
y &= -4x \quad \text{(Equation 1)} \\
y &= -5x + 5 \quad \text{(Equation 2)}
\end{aligned}
\]
**Step 1: Substitute Equation 1 into Equation 2**
Since both equations are equal to \( y \), set them equal to each other:
\[
-4x = -5x + 5
\]
**Step 2: Solve for \( x \)**
Add \( 5x \) to both sides to gather like terms:
\[
-4x + 5x = 5
\]
\[
x = 5
\]
**Step 3: Substitute \( x = 5 \) back into Equation 1 to find \( y \)**
\[
y = -4x = -4(5) = -20
\]
**Solution:**
\[
\boxed{\,x = 5,\quad y = -20\,}
\]
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Simplify this solution Bonus Knowledge
To solve the system by substitution, we start with the equations: 1. \( y = -4x \) 2. \( y = -5x + 5 \) Since both equations equal \( y \), we can set them equal to each other: \[ -4x = -5x + 5 \] Next, we can isolate \( x \). Adding \( 5x \) to both sides gives: \[ -4x + 5x = 5 \] This simplifies to: \[ x = 5 \] Now that we have the value of \( x \), we can substitute it back into one of the original equations to find \( y \). We'll use the first equation: \[ y = -4(5) = -20 \] Thus, the solution to the system is: \[ (x, y) = (5, -20) \]
