Question

Solving using elimination (algebra 1)
x - y = 11
2x + y = 19

Answer 1

To solve the system of equations using the elimination method, we have:

1. \( x - y = 11 \) (Equation 1)
2. \( 2x + y = 19 \) (Equation 2)

We can eliminate \( y \) by adding both equations together. To do this, we'll first manipulate Equation 1 so that we can directly add it to Equation 2.

From Equation 1, we can solve for \( y \):

\[
y = x - 11
\]

Now substitute this expression for \( y \) into Equation 2:

\[
2x + (x - 11) = 19
\]

Now, simplify and solve for \( x \):

\[
2x + x - 11 = 19
\]
\[
3x - 11 = 19
\]
\[
3x = 19 + 11
\]
\[
3x = 30
\]
\[
x = 10
\]

Now that we have \( x \), we can find \( y \) by substituting \( x \) back into Equation 1:

\[
x - y = 11
\]
\[
10 - y = 11
\]
\[
-y = 11 - 10
\]
\[
-y = 1
\]
\[
y = -1
\]

So the solution to the system of equations is:

\[
\boxed{(10, -1)}
\]