Question
6). \[ \left\{\begin{array}{l}\ny=-5 \\ 8 x+5 y=-17 \end{array}\right. \]
Ask by Barrett Graham. in the United States
Feb 03,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
The solution is \( x = 1 \) and \( y = -5 \).
Solution
To solve the given system of equations:
\[
\begin{cases}
y = -5 \\
8x + 5y = -17
\end{cases}
\]
**Step 1:** From the first equation, we already have the value of \( y \):
\[
y = -5
\]
**Step 2:** Substitute \( y = -5 \) into the second equation to find \( x \):
\[
8x + 5y = -17
\]
\[
8x + 5(-5) = -17
\]
\[
8x - 25 = -17
\]
**Step 3:** Solve for \( x \):
\[
8x = -17 + 25
\]
\[
8x = 8
\]
\[
x = \frac{8}{8}
\]
\[
x = 1
\]
**Solution:**
\[
x = 1 \quad \text{and} \quad y = -5
\]
Reviewed and approved by the UpStudy tutoring team
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Simplify this solution Beyond the Answer
To solve the system of equations, we first substitute the value of \( y \) from the first equation into the second equation. Since \( y = -5 \), we can replace \( y \) in the second equation: \[ 8x + 5(-5) = -17 \] This simplifies to: \[ 8x - 25 = -17 \] Now, add 25 to both sides: \[ 8x = 8 \] Dividing both sides by 8 gives us: \[ x = 1 \] So, the solution to the system of equations is \( x = 1 \) and \( y = -5 \). Now, remember to always check your solution by plugging these values back into the original equations! Doing so verifies that \( 8(1) + 5(-5) = 8 - 25 = -17 \), confirming that both equations are satisfied. Happy solving!
