Question

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

x + y + 2 = 0

3x − 4y = 15

Answer 1

Step 1: Convert to slope-intercept form

Equation 1:

x + y + 2 = 0

y = −x − 2

Equation 2:

3x − 4y = 15

−4y = −3x + 15

y = `(3x − 15)/4`

Step 2:

Table for equation: y = −x − 2

Calculation	(x, y)
y = −(−4) − 2 = 2	(−4, 2)
y = −(−2) − 2 = 0	(−2, 0)
y = −0 − 2 = −2	(0, −2)
y = −1 − 2 = −3	(1, −3)
y = −2 − 2 = −4	(2, −4)
y = −4 − 2 = −6	(4, −6)

Table for equation: y = `(3x − 15)/4`

Calculation	(x, y)
y = `(3(1) − 15)/4` = −3	(1, −3)
y = `(3(3) − 15)/4` = −1.5	(3, −1.5)
y = `(3(5) − 15)/4` = 0	(5, 0)
y = `(3(7) − 15)/4` = 1.5	(7, 1.5)
y = `(3(9) − 15)/4` = 3	(9,3)

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