To solve the system of equations using the elimination method, we have:
- \( x - y = 11 \) (Equation 1)
- \( 2x + y = 19 \) (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:
\[ \boxed{(10, -1)} \]
1 answer