Solve using the graphing method?

Question

1. y=-2x+10 
y=- 1/2x+1 

2. 
2x+3y=-18 
x-3y=-9

Answer 1

Graphing method

1) The equations are y = -2x + 10 and y = - x/2 + 1

First line y = - 2x + 10

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

slope = -2 and y -intercept is 10.

y -intercept is 10, so the line crosses the y -axis at (0, 10)

Using slope find the next point.

Slope = rise/run = -2

Start at point (0, 10), move 2 units down and 1 unit right, then plot the point (1, 8).

Draw a line through these points.

Now  the second line y = - x/2 + 1

slope = -1/2 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 = -1/2

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

Draw a line through these points.

From the graph the lines are intersecting at (6,-2).

Solution x = 6 and  y = - 2.

Answer 2

2) The equations are 2x + 3y= - 18 and x - 3y = - 9

First line 2x + 3y = - 18

Write the equation in slope-intercept form y = - 2x/3 - 6.

slope = -2/3 and y -intercept is - 6.

y -intercept is - 6, so the line crosses the y -axis at (0, - 6)

Using slope find the next point.

Slope = rise/run = 2/-3

Start at point (0, -6), move 2 units up and 3 unit left, then plot the point (1, 8).

Draw a line through these points.

Now  the second line x - 3y = - 9

y = x/3 + 3

slope = 1/3 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 = -1/-3

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

Draw a line through these points.

From the graph the lines are intersecting at (-9,0).

Solution x = - 9 and  y = 0.