Is (−2, 6)

Question

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)
.

GPT-4o mini · Answer

To determine if $(-2, 6)$ is a solution to the system of equations, we need to substitute $x = -2$ and $y = 6$ into both equations and see if they are satisfied. 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 by the point $(-2, 6)$, we can conclude that $(-2, 6)$ is indeed a solution to the system of equations. Therefore, the correct response is: **Yes, because the graphs intersect at (−2, 6)**.