Solving Systems of Equations by Graphing Quick Check 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 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) . 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 . Yes, because the graphs intersect at (−2, 6) .
No, because the graphs don’t intersect at (−2, 6).
are you sure?
No, because the graphs intersect at (-2, 6).
To determine if the point (-2, 6) is a solution to the system of linear equations x + 2y = 10 and 3x + y = 0, we need to check if these equations are satisfied when x = -2 and y = 6.
First, let's substitute x = -2 and y = 6 into the first equation:
-2 + 2(6) = 10
-2 + 12 = 10
10 = 10
The result is true, so (-2, 6) satisfies the first equation.
Next, let's substitute x = -2 and y = 6 into the second equation:
3(-2) + 6 = 0
-6 + 6 = 0
0 = 0
Again, the result is true, so (-2, 6) satisfies the second equation as well.
Since (-2, 6) satisfies both equations, it is indeed a solution to the system of linear equations x+2y=10 and 3x+y=0.
Therefore, the correct response is: Yes, because the graphs intersect at (-2, 6).