Pregunta
6. What is the x coordinate of the solution to the system of equations displayed below? \[ \left\{\begin{array}{l}3 x+4 y=36 \\ y=-\frac{1}{2} x+8\end{array}\right. \]
Ask by Simmons Klein. in the United States
Jan 27,2025
Solución de tutoría real
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The \( x \)-coordinate of the solution is 4.
Solución
To solve the system of equations:
\[
\begin{cases}
3x + 4y = 36 \\
y = -\frac{1}{2}x + 8
\end{cases}
\]
**Step 1: Substitute the expression for \( y \) from the second equation into the first equation.**
\[
3x + 4\left(-\frac{1}{2}x + 8\right) = 36
\]
**Step 2: Distribute the 4 in the equation.**
\[
3x - 2x + 32 = 36
\]
**Step 3: Combine like terms.**
\[
x + 32 = 36
\]
**Step 4: Solve for \( x \).**
\[
x = 36 - 32 \\
x = 4
\]
**Answer:** The \( x \)-coordinate of the solution is **4**.
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Simplifique esta solución Bonus Knowledge
To find the x-coordinate of the solution to the system of equations, we can substitute the expression for \( y \) from the second equation into the first equation. The substitution gives us: \[ 3x + 4\left(-\frac{1}{2}x + 8\right) = 36. \] Simplifying this, we get: \[ 3x - 2x + 32 = 36 \] \[ x + 32 = 36 \] \[ x = 36 - 32 \] \[ x = 4. \] So, the x-coordinate of the solution is \( 4 \). Now, don’t forget to find the corresponding y-coordinate by plugging \( x = 4 \) back into either equation! Happy solving!
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