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Is (−2, 6)

a solution to the system of these linear equations: x+2y=10
and 3x+y=0
? Why?(1 point)
Responses

No, because the graphs don’t intersect at (−2, 6)
.
No, because the graphs don’t intersect at left parenthesis negative 2 comma 6 right parenthesis .

Yes, because the graphs don’t intersect at (−2, 6)
.
Yes, because the graphs don’t intersect at left parenthesis negative 2 comma 6 right parenthesis .

No, because the graphs intersect at (−2, 6)
.
No, because the graphs intersect at left parenthesis negative 2 comma 6 right parenthesis .

Yes, because the graphs intersect at (−2, 6)
.
Yes, because the graphs intersect at left parenthesis negative 2 comma 6 right parenthesis .

1 answer

To determine if \((-2, 6)\) is a solution to the system of equations \(x + 2y = 10\) and \(3x + y = 0\), we need to substitute \(x = -2\) and \(y = 6\) into both equations:

  1. For the first equation \(x + 2y = 10\): \[ -2 + 2(6) = -2 + 12 = 10 \] This equation is satisfied.

  2. For the second equation \(3x + y = 0\): \[ 3(-2) + 6 = -6 + 6 = 0 \] This equation is also satisfied.

Since both equations are satisfied with the point \((-2, 6)\), this point is indeed a solution to the system of equations.

Therefore, the correct response would be: Yes, because the graphs intersect at (-2, 6).