https://file.aiquickdraw.com/mathbot/file/17253307928459bvs7667.jpg

To solve the system of equations using the elimination method, let's carefully extract the equations from the image and then solve them step by step.

The system of equations extracted from the image is:

\[
9x - 15y = 42
\]
\[
10x + 15y = 57
\]

### Step 1: Add the Equations

To eliminate \(y\), we'll add both equations together:

\[
(9x - 15y) + (10x + 15y) = 42 + 57
\]

Simplify:

\[
9x + 10x = 99
\]
\[
19x = 99
\]

### Step 2: Solve for \(x\)

Now, divide both sides by 19:

\[
x = \frac{99}{19}
\]
\[
x = 5.21 \, (\text{approximately})
\]

### Step 3: Substitute \(x\) into one of the original equations

Next, substitute \(x = 5.21\) back into one of the original equations to solve for \(y\). We can use the first equation:

\[
9(5.21) - 15y = 42
\]
\[
46.89 - 15y = 42
\]

### Step 4: Solve for \(y\)

Now, subtract 46.89 from both sides:

\[
-15y = 42 - 46.89
\]
\[
-15y = -4.89
\]

Finally, divide by -15:

\[
y = \frac{-4.89}{-15}
\]
\[
y = 0.33 \, (\text{approximately})
\]

### Solution

The approximate solution to the system of equations is:
\[
x \approx 5.21, \quad y \approx 0.33
\]

If you have any questions or need further details, feel free to ask!

### Related Questions:
1. What is the difference between the elimination method and the substitution method?
2. How would you solve the system of equations if you were to graph them?
3. What happens if the system of equations has no solution?
4. Can you use the elimination method if the coefficients of \(y\) were different?
5. How can you check if the solution is correct?

### Tip:
When solving systems of equations using elimination, always ensure the coefficients of one variable are opposite so that they cancel out when added.

Learn how to solve a system of equations using the elimination method with a detailed step-by-step guide. This problem covers key concepts in algebra, including eliminating variables and solving linear equations. Suitable for Grades 9-12.

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