Question

y = 2x - 7
4x + y = 11
which ordered pair makes both true

Answer 1

To find the ordered pair that makes both equations true, we can solve the system of equations given. The two equations are:

1. \( y = 2x - 7 \) (Equation 1)
2. \( 4x + y = 11 \) (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.