Question

Taking scale 2 cm = 1 unit, draw the graph of the following and find the solution set.

x + 3y = 5

2x − y = 3

Answer 1

Step 1: Convert to slope-intercept form (y = mx + c)

Equation 1:

x + 3y = 5

3y = 5 − x

y = `(5 − x)/3`

Equation 2:

2x − y = 3

− y = 3 − 2x

y = 2x − 3

Step 2: Make Table of Values

For y = `(5 − x)/3`

x	Calculation	y	(x, y)
0	`(5 − 0)/3`	1.67	(0, 1.67)
2	`(5 − 2)/3`	1	(2, 1)
5	`(5 − 5)/3`	0	(5, 0)

For y = 2x − 3

x	Calculation	y	(x, y)
0	2(0) − 3	−3	(0, −3)
2	2(2) − 3	1	(2, 1)
3	2(3) − 3	3	(3, 3)

The two lines intersect at the point (2, 1).

x = 2, y = 1