To determine whether the point [tex]\((-2, 6)\)[/tex] is a solution to the system of linear equations:
1. [tex]\( x + 2y = 10 \)[/tex]
2. [tex]\( 3x + y = 0 \)[/tex]
we need to see if substituting [tex]\( x = -2 \)[/tex] and [tex]\( y = 6 \)[/tex] into both equations satisfies them.
### Checking the First Equation:
Substitute [tex]\( x = -2 \)[/tex] and [tex]\( y = 6 \)[/tex] into [tex]\( x + 2y = 10 \)[/tex]:
[tex]\[ -2 + 2(6) = -2 + 12 = 10 \][/tex]
This simplifies to:
[tex]\[ 10 = 10 \][/tex]
This is true, so the point [tex]\((-2, 6)\)[/tex] satisfies the first equation.
### Checking the Second Equation:
Substitute [tex]\( x = -2 \)[/tex] and [tex]\( y = 6 \)[/tex] into [tex]\( 3x + y = 0 \)[/tex]:
[tex]\[ 3(-2) + 6 = -6 + 6 = 0 \][/tex]
This simplifies to:
[tex]\[ 0 = 0 \][/tex]
This is also true, so the point [tex]\((-2, 6)\)[/tex] satisfies the second equation.
Since [tex]\((-2, 6)\)[/tex] satisfies both equations, it is indeed a solution to the system of linear equations.
Therefore, the correct answer is:
Yes, because the graphs intersect at [tex]\((-2, 6)\)[/tex].
