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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)
.

1 answer

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

  1. \( x + y = 4 \)
  2. \( 2x + 3y = 7 \)

we need to substitute \( x = 5 \) and \( y = -1 \) into both equations and see if they hold true:

For the first equation:

\[ 5 + (-1) = 4 \]

This simplifies to:

\[ 4 = 4 \quad \text{(True)} \]

For the second equation:

\[ 2(5) + 3(-1) = 7 \]

This simplifies to:

\[ 10 - 3 = 7 \]

This further simplifies to:

\[ 7 = 7 \quad \text{(True)} \]

Since both equations are satisfied by the point (5, -1), we conclude that:

Yes, (5, -1) is a solution to the system of equations.

The best response from the options provided is:

Yes, because the graphs intersect at (5,−1).