Question
2. If \( x+y=-10 \) and \( x-y=2 \), what is the value of \( x \) ?
Ask by Pena Mullins. in the United States
Feb 03,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
\( x = -4 \)
Solution
To find the value of \( x \) given the system of equations:
\[
\begin{cases}
x + y = -10 \\
x - y = 2
\end{cases}
\]
**Step 1: Add the two equations**
\[
(x + y) + (x - y) = -10 + 2
\]
Simplifying the left side:
\[
2x = -8
\]
**Step 2: Solve for \( x \)**
\[
x = \frac{-8}{2} = -4
\]
**Answer:** \( x = -4 \)
Reviewed and approved by the UpStudy tutoring team
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Simplify this solution Bonus Knowledge
To solve the system of equations \( x + y = -10 \) and \( x - y = 2 \), we can use the method of elimination or substitution. First, let's add the two equations together: \[ (x + y) + (x - y) = -10 + 2 \] This simplifies to: \[ 2x = -8 \] Dividing both sides by 2 gives: \[ x = -4 \] Now we can find the value of \( y \) by substituting \( x = -4 \) back into one of the original equations. Using \( x + y = -10 \): \[ -4 + y = -10 \] Adding 4 to both sides gives: \[ y = -6 \] Thus, the value of \( x \) is: \[ \boxed{-4} \]
