https://file.aiquickdraw.com/mathbot/file/17263111691942nalpts2.jpg

The system of linear equations given in the image is:

1. \(7x + 2y = -61\)
2. \(-10x + y = 91\)

To solve these equations for \(x\) and \(y\), we can use the method of substitution or elimination. I will use elimination in this case:

### Step 1: Make the coefficients of \(y\) equal
Multiply the second equation by 2 to match the coefficient of \(y\) in the first equation:

\[
-20x + 2y = 182
\]

### Step 2: Add the equations to eliminate \(y\)
Add this equation to the first equation:

\[
7x + 2y - 20x + 2y = -61 + 182
\]
\[
-13x + 4y = 121
\]

### Step 3: Solve for \(x\)
Since \(4y\) cancels out, solve for \(x\):

\[
-13x = 121 \implies x = \frac{121}{-13} = -\frac{121}{13}
\]

### Step 4: Substitute \(x\) back into the second original equation to find \(y\)
\[
-10 \left(-\frac{121}{13}\right) + y = 91
\]
\[
\frac{1210}{13} + y = 91
\]
\[
y = 91 - \frac{1210}{13}
\]
\[
y = 91 - 93.077 = -2.077 \approx -\frac{27}{13}
\]

### Answer:
\(x = -\frac{121}{13}\) and \(y = -\frac{27}{13}\)

Do you need any further details on this solution, or do you have any other questions?

Here are some related questions you might consider:

1. Would you like to learn another method to solve this system, such as substitution?
2. Are you interested in checking the solution by substituting back into the original equations?
3. Do you want to explore how to graphically represent these equations?
4. Would you like to solve another system of equations?
5. Can I help you with any other mathematical problems?

**Tip:** When using elimination to solve systems of equations, it's often helpful to simplify the equations first, if possible, to make calculations easier.

Solve the system of equations: 7x + 2y = -61 and -10x + y = 91.

Explore how to solve the system of equations 7x + 2y = -61 and -10x + y = 91 using the elimination method. Detailed steps include multiplying equations, eliminating variables, and solving for x and y. Suitable for high school students in Grades 9-12.

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