Using a graph to solve the given system of equations

Question

2x−2y=−4

2x+3y=16

Answer 1

2x-2y=-4

x-y=-2

y=x+2

2x+3y=16

3y=-2x+16

y=-2x/3 +16/3

set the 2 equations equal

x+2=-2x/3+16/3

5x/3=10/3

x/3=2/3

x=2

y=x+2=2+2=4

the 2 lines intersect at the point (2,4)

1st line is upward sloping with y intercept=(0,2), slope = 1

as x increases by 2, y increases by 2 to get(0+2, 2+2)= (2,4)

2nd line is downward sloping with intercept y= (0,5 1/3), slope = -2/3

as x increases by 2, y decreases by 2(-2/3)=-4/3=-1 1/3. 5 1/3-1 1/3 =4 to get (0+2, 5 1/3- 1 1/3)= (2,4)

they intersect in quadrant I

use a graphing calculator

or graph the 2 lines by hand