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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 intersect at (−2, 6)
.
No, because the graphs 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 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 intersect at (−2, 6)
.

1 answer

To determine if \((-2, 6)\) is a solution to the system of equations given by

  1. \(x + 2y = 10\)
  2. \(3x + y = 0\)

we can substitute \(x = -2\) and \(y = 6\) into both equations.

Testing the first equation: \[ x + 2y = 10 \] Substituting in the values, we get: \[ -2 + 2(6) = -2 + 12 = 10 \] This equation is satisfied.

Testing the second equation: \[ 3x + y = 0 \] Substituting in the values, we get: \[ 3(-2) + 6 = -6 + 6 = 0 \] This equation is also satisfied.

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

Thus, the correct response is:

Yes, because the graphs don’t intersect at \((-2, 6)\).

(Note that the phrasing "the graphs don’t intersect at \((-2, 6)\)" is somewhat misleading; it's better phrased as "this point is on both lines" or "this point is a common solution.")