Systems of Linear Equations Online Practice

Question

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1 of 131 of 13 Items
Question
Is (5,−1) a solution to the system of these linear equations: x+y=4 and 2x+3y=7? Why?(1 point)
Responses

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 .

Yes, because the graphs don’t intersect at (5,−1).
Yes, because the graphs don’t intersect at left parenthesis 5 comma negative 1 right parenthesis .

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 intersect at (5,−1).
No, because the graphs intersect at left parenthesis 5 comma negative 1 right parenthesis .
Remaining Attempts : 3

Answer 1

To determine whether (5, -1) is a solution to the system of linear 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: \[ 4 = 4 \] This is true.

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

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

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