Question
12. \( \left\{\begin{array}{l}4 x-y=-4 \\ 5 x=2 y+1\end{array}\right. \)
Ask by Curry Chambers. in the United States
Feb 03,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
The solution to the system of equations is \( x = -3 \) and \( y = -8 \).
Solution
To solve the system of equations:
\[
\begin{cases}
4x - y = -4 \quad \text{(1)} \\
5x = 2y + 1 \quad \text{(2)}
\end{cases}
\]
**Step 1: Express \( y \) in terms of \( x \) from Equation (1).**
\[
4x - y = -4 \\
\Rightarrow y = 4x + 4 \quad \text{(3)}
\]
**Step 2: Substitute Equation (3) into Equation (2).**
\[
5x = 2y + 1 \\
5x = 2(4x + 4) + 1 \\
5x = 8x + 8 + 1 \\
5x = 8x + 9
\]
**Step 3: Solve for \( x \).**
\[
5x - 8x = 9 \\
-3x = 9 \\
x = -3
\]
**Step 4: Substitute \( x = -3 \) back into Equation (3) to find \( y \).**
\[
y = 4(-3) + 4 \\
y = -12 + 4 \\
y = -8
\]
**Solution:**
\[
x = -3, \quad y = -8
\]
Reviewed and approved by the UpStudy tutoring team
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Simplify this solution Mind Expander
To solve the system of equations, we can rearrange the first equation for \( y \): From \( 4x - y = -4 \), we get \( y = 4x + 4 \). Now, we can substitute this expression for \( y \) into the second equation: \( 5x = 2(4x + 4) + 1 \). Simplifying gives us \( 5x = 8x + 8 + 1 \), leading to \( 5x = 8x + 9 \), which can be rewritten as \( 5x - 8x = 9 \). Therefore, we find \( -3x = 9 \) or \( x = -3 \). Now, substituting \( x = -3 \) back into the expression for \( y \): \( y = 4(-3) + 4 = -12 + 4 = -8 \). Thus, the solution to the system is \( (x, y) = (-3, -8) \).
