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 =
= 2
substitute x = 2 into equation (1)
2 + y = 5 ⇒ y = 5 - 2 = 3
thus T = (2, 3)