Question

Draw the graph of the lines represented by the equations 2x - y = 8 and 4x + 3y = 6 on the same graph. Find the co-ordinates of the point where they intersect.

Answer 1

We have
2x - y = 8
⇒ -y = 8 - 2x
⇒ y = 2x - 8
When
x = -2
⇒ y = -4 - 8
= -12
When 
x = 0
⇒ y = -8
When
x = 2
⇒ y = 4 - 8
= -4

x	-2	-1	0	1	2
y	-12	-10	-8	-6	-4

Thus ordered pairs of 2x - y = 8 are {(-2, -12), (-1, -10), (0, -8), (1, -6), (2, -4)}.
Also,
4x + 3y = 6
⇒ 3y = 6 - 4x

⇒ y = `(6 - 4x)/(3)`
When x = -2

⇒ y = `(6 + 8)/(3)` = 4.66
When x = 0

⇒ y = `(6)/(3)` = 2
When x = 2

⇒ y = `(6 - 8)/(3)` = -0.66

x	-2	-1	0	1	2
y	4.66	3.33	2	0.66	-0.66

Thus ordered pairs of 4x + 3y = 6 are {(-2, 4.66), (-1, 3.33), (0.2), (1, 0.66), (2, -0.66)}.

The point of intersection is (3, -2).