Question

How to solve this question?

Answer 1

T = (2, 3)

to find T, the point of intersection of the 2 lines, solve the 2 equations simultaneously.

x + y = 5 → (1)

2y - 5x = - 4 → (2)

from (1) y = 5 - x

substitute y = 5 - x into equation (2)

2(5 - x) - 5x = - 4

10 - 2x - 5x = - 4

10 - 7x = - 4

subtract 10 from both sides

- 7x = - 4 - 10 = - 14

divide both sides by - 7

x = $\frac{(- 14)}{(- 7)}$ = 2

substitute x = 2 into equation (1)

2 + y = 5 ⇒ y = 5 - 2 = 3

thus T = (2, 3)