Question
21) Solve the system by elimination \( \left\{\begin{array}{l}3 x+y=-26 \\ 2 x-y=-19\end{array}\right. \)
Ask by Campos Barker. in the United States
Jan 24,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
The solution is \( x = -9 \) and \( y = 1 \).
Solution
To solve the system of equations by elimination:
\[
\begin{cases}
3x + y = -26 \\
2x - y = -19
\end{cases}
\]
**Step 1: Add the two equations to eliminate \( y \).**
\[
(3x + y) + (2x - y) = -26 + (-19)
\]
\[
5x = -45
\]
\[
x = \frac{-45}{5} = -9
\]
**Step 2: Substitute \( x = -9 \) into one of the original equations to find \( y \). Let's use the second equation:**
\[
2x - y = -19
\]
\[
2(-9) - y = -19
\]
\[
-18 - y = -19
\]
\[
-y = -19 + 18
\]
\[
-y = -1
\]
\[
y = 1
\]
**Solution:**
\[
x = -9, \quad y = 1
\]
Or as an ordered pair:
\[
(x, y) = (-9,\ 1)
\]
Reviewed and approved by the UpStudy tutoring team
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Simplify this solution Mind Expander
To solve the system by elimination, let's add the two equations together in a way that eliminates \( y \). We start with: 1) \( 3x + y = -26 \) 2) \( 2x - y = -19 \) Adding these equations together gives us: \((3x + y) + (2x - y) = -26 - 19\) This simplifies to: \(5x = -45\) Now, divide both sides by 5: \(x = -9\) Next, we substitute \( x = -9 \) back into one of the original equations to solve for \( y \). Using the first equation: \(3(-9) + y = -26\) This simplifies to: \(-27 + y = -26\) Adding 27 to both sides, we get: \(y = 1\) Thus, the solution to the system is: \(x = -9\) and \(y = 1\).
