Systems of Linear Equations Online Practice

Question

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2 of 132 of 13 Items
Question
Is (7, 3) the solution to the system of these linear equations: 3x+2y=5 and −x+6y=11? Why?(1 point)
Responses

Yes, because the graphs intersect at (7, 3).
Yes, because the graphs intersect at left parenthesis 7 comma 3 right parenthesis .

Yes, because the graphs don’t intersect at (7, 3).
Yes, because the graphs don’t intersect at left parenthesis 7 comma 3 right parenthesis .

No, because the graphs intersect at (7, 3).
No, because the graphs intersect at left parenthesis 7 comma 3 right parenthesis .

No, because the graphs don’t intersect at (7, 3

Answer 1

To determine whether (7, 3) is a solution to the system of equations \(3x + 2y = 5\) and \(-x + 6y = 11\), we can substitute \(x = 7\) and \(y = 3\) into both equations to check if they hold true.

1. First equation: \(3x + 2y = 5\)

   Substitute \(x = 7\) and \(y = 3\):

   \[ 3(7) + 2(3) = 21 + 6 = 27 \] \(27 \neq 5\) (This equation is not satisfied.)

2. Second equation: \(-x + 6y = 11\)

   Substitute \(x = 7\) and \(y = 3\):

   \[ -7 + 6(3) = -7 + 18 = 11 \] \(11 = 11\) (This equation is satisfied.)

Since the first equation is not satisfied, (7, 3) is not a solution to the system of equations.

The correct response is:

No, because the graphs don’t intersect at (7, 3).