Question

Solve the following pair of simultaneous equations graphically.

2x − 7y = 6

5x − 8y = −4

Answer 1

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

2x − 7y = 6

y = `(2x − 6)/7`

5x − 8y = −4 

y = `(5x + 4)/8`

y = `(2x − 6)/7`       ...[For Equation (i)]

If x = −4x 

y = `(2(−4) − 6)/7`

y = `(−8 −6)/7`

= `(−14)/7`

y = −2

Point = (−4, −2)

y = `(2(3) − 6)/7`

y = `(6 − 6)/7`

y = 0

Point = (3,0)

If x = 10

y = `(2(10) − 6)/7`

y = `(20 − 6)/7`

y = `14/7`

y = `2`

Point (10, 2)

y = `(5x + 4)/8`     ...[Equation (ii)]

If x = −4x

y = `(5(−4) + 4)/8`

y = `(−20 + 4)/8`

y = `(−16)/8`

y = `−2`

Point = (−4, −2)

If x = 0

y = `(5(0) + 4)/8`

y = `4/8`

y = 0.5

If x = 4

y = `(5(4) + 4)/8`

y = `(20 + 4)/8`

y = `24/8`

y = 3

For y = `(2x − 6)/7`

x	y = `(2x − 6)/7`	(x, y)
−4	− 2	(−4, −2)
3	0	(3, 0)
10	2	(10,2)

For y = `(5x + 4)/8`

x	y = `(5x + 4)/8`	(x, y)
− 4	− 2	(−4, −2)
0	0.5	(0, 0.5)
4	3	(4, 3)