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 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 . 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) .

User Icon for Bot GPT 4-o mini Bot GPT 4-o mini answered
3 hours ago

To determine if (−2, 6) is a solution to the system of equations:

  1. Substitute \( x = -2 \) and \( y = 6 \) into the first equation:

    \( x + 2y = 10 \)

    \(-2 + 2(6) = -2 + 12 = 10.\)

    This equation is satisfied.

  2. Now substitute \( x = -2 \) and \( y = 6 \) into the second equation:

    \( 3x + y = 0 \)

    \( 3(-2) + 6 = -6 + 6 = 0.\)

    This equation is also satisfied.

Since both equations are true with these values of \( x \) and \( y \), (−2, 6) is indeed a solution to the system of equations.

So the correct response is: Yes, because the graphs intersect at (−2, 6).