Question

Systems of Linear Equations Online Practice
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Question
Is (5,−1)
a solution to the system of these linear equations: x+y=4
and 2x+3y=7
? Why?(1 point)
Responses

Yes, because the graphs intersect at (5,−1)
.
Yes, because the graphs intersect at left parenthesis 5 comma negative 1 right parenthesis .

No, because the graphs don’t intersect at (5,−1)
.
No, because the graphs don’t intersect at left parenthesis 5 comma negative 1 right parenthesis .

No, because the graphs intersect at (5,−1)
.
No, because the graphs intersect at left parenthesis 5 comma negative 1 right parenthesis .

Yes, because the graphs don’t intersect at (5,−1)
.

Answer 1

To determine if (5, -1) is a solution to the system of linear equations:

1. Substitute \(x = 5\) and \(y = -1\) into both equations.

**For the first equation:**
\[ x + y = 4 \]
\[ 5 + (-1) = 4 \]
\[ 4 = 4 \] (This is true.)

**For the second equation:**
\[ 2x + 3y = 7 \]
\[ 2(5) + 3(-1) = 7 \]
\[ 10 - 3 = 7 \]
\[ 7 = 7 \] (This is also true.)

Since (5, -1) satisfies both equations, it is indeed a solution to the system.

The correct response is:
**Yes, because the graphs intersect at (5,−1).**