y=
8x
y, equals, 2, x, minus, 12
y=
2x−12

You seem to have two equations involving \( y \) and \( x \):

1. \( y = 8x \)
2. \( y = 2x - 12 \)

To solve this system of equations, we can set the two expressions for \( y \) equal to each other since both represent \( y \):

\[
8x = 2x - 12
\]

Now, let's solve for \( x \):

1. Subtract \( 2x \) from both sides:

\[
8x - 2x = -12
\]

\[
6x = -12
\]

2. Divide both sides by 6:

\[
x = \frac{-12}{6} = -2
\]

Now that we have \( x = -2 \), substitute this value into one of the original equations to find \( y \). Using \( y = 8x \):

\[
y = 8(-2) = -16
\]

Thus, the solution is \( x = -2 \) and \( y = -16 \).

Would you like more details on the steps? Here are 5 related questions:

1. How do we verify the solution for a system of linear equations?
2. Can we graph these equations to visualize the solution?
3. What are other methods to solve systems of equations?
4. How do we solve more complex systems with three or more variables?
5. What happens if two equations in a system are parallel?

**Tip:** In a system of equations, equating the two expressions for the same variable is a common approach when solving by substitution.

Learn how to solve the system of linear equations y = 8x and y = 2x - 12 with a detailed step-by-step explanation. This solution covers key algebraic methods such as substitution and the equality of functions theorem. Suitable for students in Grades 7-9.

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