The system of equations shown below is graphed on a coordinate grid:

3y + x = 4
2y − x = 6

which statement is true about the coordinates of the point that is the solution to the system of equations?

a. it is (−2, 2) and lies on both lines.
b. it is (−5, 3) and lies on both lines.
c. it is (−5, 3) and does not lie on either line.
d. it is (−2, 2) and does not lie on either line.

3y+x=4

2y-x=6

Solve x+3y=4 for x

Add -3y to both sides

x+3y-3y=4-3y

x=-3y+4

Substitute -3y+4 for x in -x+2y=6

-x+2y=6

-(-3y+4)+2y=6

Simplify both sides of the equation

5y-4=6

Add 4 to both sides

5y-4+4=6+4

5y=10

Divide both sides by 5

5y/5=10/5

y=2

Substitute 2 for y in x=-3y+4

x=-3y+4

x=(-3)(2)+4

x= -6+4

x= -2

Answer : x=-2 and y=2

The answer is A

 it is (-2,2) and lies on both lines

I hope that's help  !

step-by-step explanation:

use pothagarean therom

a^2+b^2=c^2 so first ac

acm is a right triangle because c= 90°

and am (the hypotenuse or c) =16+9 =25

but there is not enough info we need another angle or side length