Solve the simultaneous equations: 3x + 4y = 5 and 2x – 3y = 9

To solve a simultaneous equation we use a method known as elimination. We choose to 'eliminate' or remove the X or Y term. To 'eliminate' x we must firstly determine the lowest common multiple 3 and 2 (as these are the values in front of x in both equations). The lowest common multiple is 6. Therefore, we multiple the first equation by 2 and the second by 3. This gives: 6x + 8y = 10 and 6x - 9y = 27. To 'eliminate' x when can then subtract the second equation from the first. This give us: 17y=-17. Thus, y = -1. We can then substitute y = -1 into the first equation such that 3x+4=5. Rearranging this equation gives, 3x=9. Hence x=9/3=3. Therefore, x=3 and y=-1.

PG
Answered by Prasanna G. Maths tutor

5568 Views

See similar Maths GCSE tutors

Related Maths GCSE answers

All answers ▸

The straight line L1 passes through the points with coordinates (4, 6) and (12, 2) . The straight line L2 passes through the origin and has a gradient of -3. The lines L1 and L2 intersect at point P. Find the coordinates of P.


How do I tackle fractional powers?


How do you solve simultaneous equations and why do you do it?


How do you factorize a quadratic equation which has a coefficient of x^2 other than 1?


We're here to help

contact us iconContact ustelephone icon+44 (0) 203 773 6020
Facebook logoInstagram logoLinkedIn logo

MyTutor is part of the IXL family of brands:

© 2025 by IXL Learning