Question

Solve the system of equations below by graphing them with a pencil and paper. Enter your answer as an ordered pair.

y = 2x - 3 y = -2x + 5 ...?

Answer 1

Solution is (2,1)

Explanation:

In order to graph both lines ,we need to find the X and Y intercepts for both equations

Lets take equation y =2x -3

To find y intercept ,we plug x =0 ,we get y =2(0)-3 = 0-3 =-3

Y intercept is (0,-3) Which is point 'C' in the graph

To find X intercept ,we plug y =0 ,we get 0 = 2x-3 or x = 3/2 or 1.5

X intercept is (1.5,0) Which is point D in the graph.

Lets take equation y =-2x+5

To find y intercept ,we plug x =0 ,we get y = -2(0)+5 = 0+5 = 5

Y intercept is (0,5) which is point A in the graph .

To find X intercept ,we plug y =0 ,we get 0 =-2x+5 or x = 5/2 or 2.5

X intercept is (2.5,0) which is point B on the graph

After getting intercept of both lines ,we plot both lines

In the graph Blue line shows y=2x-3 and Red line shows y =-2x+5

both lines intersect at point E which is called the solution of both equation

which is given to be (2,1)

Answer 2

y = 2x - 3 . . . (1)
y = -2x + 5 . . . (2)
Equating (1) and (2),
2x - 3 = -2x + 5
2x + 2x = 5 + 3
4x = 8
x = 8/4 = 2
x = 2
y = 2(2) - 3 = 4 - 3 = 1
y = 1

Solution = (2, 1)