Question

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

2x + 3y + 2 = 0

4x + 5y = 0

Answer 1

Step 1: Convert to slope-intercept form

Equation 1:

2x + 3y + 2 = 0

3y = −2x − 2

y = `− 2/3x − 2/3`

Equation 2:

4x + 5y = 0

5y = −4x

y = `−4/5 x`

Step 2:

Tables for equation: y = `− 2/3x − 2/3`

Calculation	(x, y)
y = `−2/3(−3) − 2/3 = 2 − 2/3 = 4/3`	(−3, 1.33)
y = `− 2/3(0) − 2/3 = −2/3`	(0, −0.67)
y = `−2/3(3) − 2/3 = −2 − 2/3 = −8/3`	(3, −2.67)
y = `−2/3(5) −2/3 = −10/3 = − 2/3 = −12/3`	(5, −4)

Tables for equation: y = `−4/5 x`

Calculation	(x, y)
y = `− 4/5 (−5) = 4`	(−5, 4)
y = `− 4/5(0) = 0`	(0, 0)
y = `−4/5(5) = −4`	(5, −4)

The two lines intersect at the point (5, −4).