Question

Solve the following pair of simultaneous equations graphically.

3y − 2x = 7

5x + 3y + 7 = 0

Answer 1

Given:

3y − 2x = 7

5x + 3y + 7 = 0

Step 1: Convert into slope–intercept form (y = mx + c)

Equation 1:

3y − 2x = 7

3y = 2x + 7

y = `2/3x + 7/3`

Equation 2:

5x + 3y + 7 = 0

3y = −5x − 7

y = `(−5)/3x − 7/3`

Step 2: Make Tables of Values

For y = `2/3x + 7/3`

x	Calculation	y	(x, y)
0	`(2(0))/3 + 7/3`	2.33	(0, 2.33)
−2	`(2(−2))/3 + 7/3 = (−4 + 7)/3`	1	(−2, 1)
2	`4/3 + 7/3 = 11/3`	3.67	(2, 3.67)

For y = `(−5)/3x − 7/3`

x	Calculation	y	(x, y)
0	`(−5(0))/3 − 7/3`	2.33	(0, −2.33)
−2	`(−5(−2))/3 − 7/3 = (10 − 7)/3`	1	(−2, 1)
2	`(−10)/3 − 7/3 = 17/3`	−5.67	(2, −5.67)

The lines intersect at point (−2,1)

∴ x = −2, y = 1