Question

Write down the coordinates of the point of intersection of the two lines whose equations are 3x+2y=10 2x-6y=3 (1 mark)

Answer 1

(3,
`(1)/(2)` )

Explanation:

to find the point of intersection, solve the equations simultaneously.

3x + 2y = 10 → (1)

2x - 6y = 3 → (2)

multiplying (1) by 3 and adding to (2) will eliminate y

9x + 6y = 30 → (3)

add (2) and (3) term by term to eliminate y

11x + 0 = 33

11x = 33 ( divide both sides by 11 )

x = 3

substitute x = 3 into either of the 2 equations and solve for y

substituting into (1)

3(3) + 2y = 10

9 + 2y = 10 ( subtract 9 from both sides )

2y = 1 ( divide both sides by 2 )

y =
`(1)/(2)`

solution is (3,
`(1)/(2)` )