Question

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

4x + 3y = 5

x − 2y + 7 = 0

Answer 1

Step 1: Convert to Slope-Intercept Form

4x + 3y = 5 

y = `(−4x + 5)/3`

x − 2y = −7

y = `(x + 7)/2`

Equation 1: 4x + 3y = 5

Choose easy values for x

x	y = `bb(−4x + 5)/3`	(x, y)
−2	`(−4(−2) + 5)/3 = 13/3`	(−2, 4.33)
−1	`(−4(−1) + 5)/3 = 9/3`	(−1, 3)
0	`5/3` = 1.67	(0, 1.67)
1	`1/3` = 0.33	(1, 0.33)
2	`−3/3` = −1	(2, −1)

For Equation 2: x − 2y = −7

x	y = `bb(x + 7)/2`	(x, y)
−3	`(−3 + 7)/2 = 4/2` = 2	(−3, 2)
−2	`(−2 + 7)/2 = 5/2` = 2.5	−2, 2.5
−1	`(−1 + 7)/2 = 6/2` = 3	(−1, 3)
0	`7/2 = 3.5`	(0, 3.5)
1	`8/2` = 4	(1, 4)

The two lines intersect at the point (−1,3).