Question

Here is a system of linear equations:
-2x + y = 7 6x + y = 11

What is the solution to the system of equations shown?

Answer 1

To solve the system of equations:

1. \(-2x + y = 7\) (Equation 1)
2. \(6x + y = 11\) (Equation 2)

We can use the elimination or substitution method. Here, we'll use the elimination method.

First, we can eliminate \(y\) by subtracting Equation 1 from Equation 2:

\[
(6x + y) - (-2x + y) = 11 - 7
\]

This simplifies to:

\[
6x + y + 2x - y = 4
\]

Which simplifies to:

\[
8x = 4
\]

Now, divide both sides by 8:

\[
x = \frac{4}{8} = \frac{1}{2}
\]

Next, we substitute \(x = \frac{1}{2}\) back into one of the original equations to find \(y\). We'll use Equation 1:

\[
-2\left(\frac{1}{2}\right) + y = 7
\]

This simplifies to:

\[
-1 + y = 7
\]

Now, add 1 to both sides:

\[
y = 7 + 1 = 8
\]

Thus, the solution to the system of equations is:

\[
\boxed{\left(\frac{1}{2}, 8\right)}
\]