Is (−2, 6)

Question

(
−
2
,

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

No, because the graphs don’t intersect at (−2, 6)
(
−
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)
(
−
2
,

6
)
.
Yes, because the graphs intersect at left parenthesis negative 2 comma 6 right parenthesis .

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

Answer 1

To determine if the point \((-2, 6)\) is a solution to the system of equations \(x + 2y = 10\) and \(3x + y = 0\), we can substitute \(x = -2\) and \(y = 6\) into both equations.

1. For the first equation \(x + 2y = 10\): \[ -2 + 2(6) = -2 + 12 = 10 \] This is true.

2. For the second equation \(3x + y = 0\): \[ 3(-2) + 6 = -6 + 6 = 0 \] This is also true.

Since \((-2, 6)\) satisfies both equations, it is a solution to the system.

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