Question

Draw the graph of the lines represented by the equations 3x - 2y = 4 and x + y = 3 on the same graph. Find the coordinates of the point where they intersect. State, whether the lines are perpendicular to each other.

Answer 1

We have
3x - 2y = 4
⇒ -2y = 4 - 3x
⇒ 2y = 3x - 4

⇒ y = `(3x - 4)/(2)`
When x = -2

⇒ y = `(-6 - 4)/(2)` = -5
When x = 0

⇒ y = `-(4)/(2)` = -2
When x = 2

⇒ y = `(6 - 4)/(2)` = 1

x	-2	-1	0	1	2
y	-5	-3.5	-2	-0.5	1

Thus ordered pairs of 3x - 2y = 4 are {(-2, -5), (-1, -3.5). (0, -2), (1, -0.5), (2, 1)}.
Also,
x + y = 3
⇒ y = 3 - x
When x = -2
⇒ y = 4 + 2
 = 6
When x = 0
⇒ y = 3
When x = 2
⇒ y = 4 - 2
= 2

x	-2	-1	0	1	2
y	5	4	3	2	1

Thus ordered pairs of x + y = 3 are {(-2, 5), (-1, 4), (0, 3), (1, 2), (2, 1)}.

The point of intersection is (2, 1).