Question

The system of equations shown below is graphed on a coordinate grid: 4y + x = 4 2y − x = 8 Which statement is true about the coordinates of the point that is the solution to the system of equations? It is (2, 5) and lies on both lines. It is (−4, 2) and lies on both lines. It is (2, 5) and does not lie on either line. It is (−4, 2) and does not lie on either line

Answer 1

It is (−4, 2) and lies on both lines.

Explanation:

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

4y + x = 4

2y − x = 8

(a) (2, 5), Plug in x= 2 and y=5 in the given equations

4(5) + 2 = 4 --------> false

2(5) - 2=8 --------->True

(b) (-4,2)

4(2) -4 = 4 --------> True

2(2) − (-4) = 8 ------> True

for (-4,2) both equations are true , so it lies on both lines

It is (−4, 2) and lies on both lines.

Answer 2

(2,5) is not on first line: 4*(5)+2 = 22 not 4 - first statement is false

(-4,2) is on first line: 4*(-4)-2 = -18
(-4,2) is on second line: 2*(-4)-(2) = -10 - second statement is false

(2,5) is not on second line: 2*(-5)-2 = -12 not 8 - third statement is true

(-4,2) is on bought lines - 4rd statement is false