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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.
Solution
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).
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