Solve Linear System Graphically (level2)

Question

Solve the following system of equations graphically on the set of axes below:

y= -1/2x+8

x-4y=-8

please show a picture if possible of the graph. thanks.

Answer 1

y= (-1/2)x + 8 is a downward sloping line with y intercept = 8 or (0,8)

x-4y = -8

-4y = -x=8

4y = x+8

y = (1/4)x +2 is an upward sloping line with y intercept = 2 or the point (0,2)

they intersect where -x/2 + 8 = x/4 + 2 or

3x/4 = 6

x=(4/3)6 = 8

y= (1/4)8 + 2 = 4

they intersect at the point (8,4)

plot the point (0,2) and (8.4) draw a line connecting them

plot the point (0,8) and (8,4) draw a line connecting them.

(8,4) is where the two lines intersect