https://file.aiquickdraw.com/mathbot/file/17253309368076c6y5sp5.jpg

The image you provided contains a system of linear equations. Let's extract and solve it using the elimination method.

The equations visible in the image are:

\[
\begin{aligned}
1. \quad 3a - 2b - 36 &= 10 \\
2. \quad 5a - 3b - 46 &= 4
\end{aligned}
\]

First, let's rewrite these equations in standard form:

\[
\begin{aligned}
1. \quad 3a - 2b &= 46 \quad \text{(Adding 36 to both sides)} \\
2. \quad 5a - 3b &= 50 \quad \text{(Adding 46 to both sides)}
\end{aligned}
\]

Now, we'll use the elimination method. To eliminate one variable, we'll multiply the first equation by 3 and the second equation by 2 so that the coefficients of \(b\) will be opposites.

\[
\begin{aligned}
1. \quad 9a - 6b &= 138 \quad \text{(Multiplying the first equation by 3)} \\
2. \quad 10a - 6b &= 100 \quad \text{(Multiplying the second equation by 2)}
\end{aligned}
\]

Next, subtract the second equation from the first:

\[
\begin{aligned}
(9a - 6b) - (10a - 6b) &= 138 - 100 \\
- a &= 38
\end{aligned}
\]

So,

\[
a = -38
\]

Now, substitute \(a = -38\) back into one of the original equations to solve for \(b\). Using the first equation:

\[
3(-38) - 2b = 46
\]

Simplify:

\[
-114 - 2b = 46
\]

Add 114 to both sides:

\[
-2b = 160
\]

Finally, divide by -2:

\[
b = -80
\]

The solution to the system of equations is:

\[
\boxed{a = -38 \text{ and } b = -80}
\]

Would you like more details on this solution, or do you have any questions?

### Relative Questions:
1. How does the elimination method compare to the substitution method in solving systems of equations?
2. Can you verify the solution by substituting the values of \(a\) and \(b\) back into both original equations?
3. What would be the next step if the coefficients of \(b\) were not easily eliminated?
4. How does solving a system of equations graphically compare to the elimination method?
5. How can you apply the elimination method to a system of three equations with three variables?

### Tip:
Always double-check your solutions by substituting the values back into the original equations to ensure they satisfy both equations.

Learn how to solve systems of linear equations using the elimination method with a step-by-step solution. This problem covers key concepts in algebra, including systems of equations and the elimination method. Suitable for students in Grades 9-12.

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