Question

P is the point of intersection of the lines with equations 5x+3y=9 and 7x -2y= 25. write down the coordinates of P

Answer 1

P (3, - 2 )

Explanation:

Solve the equations simultaneously for point of intersection P

5x + 3y = 9 → (1)

7x - 2y = 25 → (2)

Multiplying (1) by 2 and (2) by 3 and adding will eliminate the y- term

10x + 6y = 18 → (3)

21x - 6y = 75 → (4)

add (3) and (4) term by term to eliminate y

31x + 0 = 93

31x = 93 ( divide both sides by 31 )

x = 3

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

Substituting into (1)

5(3) + 3y = 9

15 + 3y = 9 ( subtract 15 from both sides )

3y = - 6 ( divide both sides by 3 )

y = - 2

Then P = (3, - 2 )