Question

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

3x + 5y = 12

3x − 5y + 18 = 0

Answer 1

Step 1: Convert to slope-intercept form

Equation 1:

3x + 5y = 12

5y = −3x + 12

y = `−3/5x + 12/5` 

Equation 2:

3x − 5y + 18 = 0

3x − 5y = − 18

−5y = −3x − 18

y = `3/5x + 18/5`

Step 2:

Tables for equation: y = `−3/5x + 12/5` 

Calculation	(x, y)
y = `−3/5 (−3) + 12/5 = (9 + 12)/5 = 21/5`	(−3, 4.2)
y = `−3/5(−1) + 12/5 = (3 + 12)/5 = 15/5`	(−1, 3)
y = `−3/5(0) + 12/5 = 12/5`	(0, 2.4)
y = `−3/5(3) + 12/5 = (−9 + 12)/5 = 3/5`	(3, 0.6)
y = `−3/5(5) + 12/5 = (−15 + 12)/5 = −3/5`	(5, −0.6)

Tables for equation: y = `3/5x + 18/5`

Calculation	(x, y)
y = `3/5(−3) + 18/5 = (−9 + 18)/5 = 9/5`	(−3, 1.8)
y = `3/5(−1) + 18/5 = (−3 + 18)/5 = 15/5`	(−1, 3)
y = `3/5(0) + 18/5 = 18/5`	(0, 3.6)
y = `3/5(2) + 18/5 = (6 + 18)/5 = 24/5`	(2, 4.8)
y = `3/5(3) + 18/5 = 9 + 18/5 = 27/5`	(3, 5.4)

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