How do i Solve the system by graphing.?

Question

x-y+2 
x+3y=-8

Answer 1

Graphing method

1) The equations are x-y +2 = 0  and x + 3y = - 8

First line x - y + 2 = 0

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

y = x + 2

slope = 1 and y -intercept is 2.

y -intercept is 2, so the line crosses the y -axis at (0, 2)

Using slope find the next point.

Slope = rise/run = -1/-1

Start at point (0, 0), move 1 unit down and 1 unit left, then plot the point (-1, 1).

Draw a line through these points.

Now  the second line x + 3y = - 8

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

y = - x/3 - 8/3

slope = - 1/3 and y -intercept is - 8/3.

y -intercept is - 8/3, so the line crosses the y -axis at (0, - 8/3)

Using slope find the next point.

Slope = rise/run =  1/-3

Start at point (0, - 8/3), move 1 unit up and 3 units left, then plot the point (-3, -5/3).

Draw a line through these points.

From the graph the lines are intersecting at (-3.5, -1.5).

Solution of the equations is x = - 3.5 and  y = - 1.5.