Questions: What is the solution to the system of equations shown?

What is the solution to the system of equations shown?
Transcript text: What is the solution to the system of equations shown?
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Solution

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Solution Steps

To solve the system of linear equations, we can use the method of substitution or elimination. Here, we will use the elimination method to eliminate one of the variables and solve for the other.

  1. Subtract the first equation from the second to eliminate \( y \).
  2. Solve for \( x \).
  3. Substitute the value of \( x \) back into one of the original equations to find \( y \).
Step 1: Write the System of Equations

We start with the given system of linear equations: \[ \begin{array}{c} x + y = -10 \\ 2x + y = -33 \end{array} \]

Step 2: Eliminate \( y \)

To eliminate \( y \), we subtract the first equation from the second: \[ (2x + y) - (x + y) = -33 - (-10) \] Simplifying, we get: \[ x = -23 \]

Step 3: Solve for \( y \)

Substitute \( x = -23 \) back into the first equation: \[ -23 + y = -10 \] Solving for \( y \), we get: \[ y = -10 + 23 = 13 \]

Final Answer

\[ \boxed{(x, y) = (-23, 13)} \]

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