To find the ordered pair that makes both equations true, we can solve the system of equations given. The two equations are:
- \( y = 2x - 7 \) (Equation 1)
- \( 4x + y = 11 \) (Equation 2)
We can substitute Equation 1 into Equation 2.
Substituting \( y \) from Equation 1 into Equation 2:
\[ 4x + (2x - 7) = 11 \]
Now, simplify and solve for \( x \):
\[ 4x + 2x - 7 = 11 \] \[ 6x - 7 = 11 \] \[ 6x = 11 + 7 \] \[ 6x = 18 \] \[ x = 3 \]
Now that we have \( x \), we can find \( y \) using Equation 1:
\[ y = 2(3) - 7 \] \[ y = 6 - 7 \] \[ y = -1 \]
Thus, the ordered pair \( (x, y) \) that satisfies both equations is:
\[ \boxed{(3, -1)} \]
To verify, we can substitute \( x = 3 \) and \( y = -1 \) back into both original equations:
For Equation 1: \[ y = 2(3) - 7 = 6 - 7 = -1 \quad \text{(True)} \]
For Equation 2: \[ 4(3) + (-1) = 12 - 1 = 11 \quad \text{(True)} \]
Both equations are satisfied, confirming that the solution \( (3, -1) \) is correct.