Solving Systems of Equations by Graphing Quick Check

Question

2 of 52 of 5 Items

Question
Is (−2, 6)
a solution to the system of these linear equations: x+2y=10
and 3x+y=0
? Why?(1 point)
Responses

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 .

Yes, because the graphs intersect at (−2, 6)
.
Yes, because the graphs 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 .

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

Answer 1

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 and see if they hold true.

1. Substitute into the first equation \(x + 2y = 10\):

   \[ -2 + 2(6) = -2 + 12 = 10 \]

   This is true.

2. Now substitute into the second equation \(3x + y = 0\):

   \[ 3(-2) + 6 = -6 + 6 = 0 \]

   This is also true.

Since both equations are satisfied, (−2, 6) is indeed a solution to the system.

Therefore, the correct response is:

Yes, because the graphs intersect at (−2, 6).