Santiago Erickson
06/18/2024 · Middle School
ons: \( 1 / 2 x-y=10, y=3 / 2 x-8 \) What is the value of \( (x) \) ?
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Tutor-Verified Answer
Step-by-step Solution
To solve the system of equations given by:
1. \( \frac{1}{2}x - y = 10 \)
2. \( y = \frac{3}{2}x - 8 \)
we can substitute the expression for \( y \) from the second equation into the first equation.
Substituting \( y \) in the first equation:
\[
\frac{1}{2}x - \left(\frac{3}{2}x - 8\right) = 10
\]
Now, simplify the equation:
\[
\frac{1}{2}x - \frac{3}{2}x + 8 = 10
\]
Combine the \( x \) terms:
\[
\left(\frac{1}{2} - \frac{3}{2}\right)x + 8 = 10
\]
This simplifies to:
\[
-\frac{2}{2}x + 8 = 10
\]
or
\[
-x + 8 = 10
\]
Now, isolate \( x \):
\[
-x = 10 - 8
\]
\[
-x = 2
\]
\[
x = -2
\]
Thus, the value of \( x \) is:
\[
\boxed{-2}
\]
Quick Answer
The value of \( x \) is -2.
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