Solve graphically the system of linear equations below. And, What is the solution to the system of linear equations?

Question

y=-2x+3 

 y=2x-1

Answer 1

The equations are y  = -2x  + 3 and y = 2x - 1

The equations are already in slope-intercept form y = mx + b , where m is slope and b is y - intercept.

First equation is y  = -2x  + 3

 y  = -2x  + 3

compare the equation with slope -intercept form y  = mx  + b.

slope = - 2 and y  - intercept is 3.

y - intercept is 3, so the line crosses the y  - axis at (0, 3)

Using slope find the next point.

Slope = rise/run = -2

Start at point (0, 3), move 2 units down and 1 unit right, then plot the point (1, 1).

Draw a line through these points.

Second equation is y  = 2x  - 1

slope =  2 and y - intercept is - 1.

y - intercept is -1, so the line crosses the y  - axis at (0, -1)

Using slope find the next point.

Slope = rise/run = 2

Start at point (0, -1), move 2 units up and 1 unit right, then plot the point (1, 1).

Draw a line through these points.

Graph :

From the graph we observe the two lines are intersect at (1,1).

Solution to the system of linear equations is x  = 1 , y  = 1.