https://file.aiquickdraw.com/mathbot/file/1728523717595xlq9lgtr.jpg

From the image, we see an exercise where values for \(x = 2\) and \(y = 8\) are plugged into two equations. The setup asks to check if these values satisfy both equations. The two equations appear to be:

1. \( y = 3x + 2 \)
2. \( 2x + y = 12 \)

Let's check if the given values \( x = 2 \) and \( y = 8 \) work in both equations.

### First Equation: 
\[
y = 3x + 2
\]
Substituting \(x = 2\) into the equation:
\[
y = 3(2) + 2 = 6 + 2 = 8
\]
So, for the first equation, \( y = 8 \), which matches the given \( y = 8 \). Hence, the first equation is satisfied.

### Second Equation: 
\[
2x + y = 12
\]
Substituting \(x = 2\) and \(y = 8\):
\[
2(2) + 8 = 4 + 8 = 12
\]
Thus, the second equation is also satisfied.

Therefore, the values \(x = 2\) and \(y = 8\) satisfy both equations.

Would you like further details or a breakdown of the steps? Here are 5 related questions you might explore:

1. What is the process of solving a system of linear equations?
2. How can we graphically interpret these two equations?
3. What happens if we change the values of \(x\) and \(y\)?
4. Can these equations represent real-world scenarios?
5. How can we solve these equations algebraically if the values were not given?

**Tip:** Always double-check your substitutions when verifying if a solution satisfies multiple equations!

Solving a system of linear equations by plugging in values for x = 2 and y = 8.

Learn how to solve a system of linear equations by checking the values x = 2 and y = 8 with detailed step-by-step verification. This problem covers key algebraic concepts, including substitution and solving simultaneous equations. Suitable for students in Grades 6-8.

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