Solve the simultaneous equations: 5x + 3y = 9 and 7x - 2y = 25.

To solve these similar equations, we must either first eliminate x or y. There are multiple ways of doing this, one being rearranging one of the equations so that it is either "x=.." or "y=..." and then substituting the rearranged equation into the other equation and so eliminating one variable. 

Specifically for this example it could be:

Rearrange 7x - 2y = 25 to 2y = 7x - 25. Then divide the entire equation by 2, giving: y = (7/2)x - (25/2). 

Now enter this new equation into the second equation in place of y and solve for x: 5x + 3y = 9 becomes 5x+3(3.5x - 12.5) = 9. Rearrange by first expanding the brackets and collecting all x on one side and then dividing by the coefficient of x to give x = 3.

Now enter this into an equation and solve for y. For instance: 5x + 3y = 9, set x=3 giving 5(3) + 3y = 9. 3y=(-6) Y=(-2) 

you can check this but entering both these values for x and y into the second equation for example. 7(3)-2(-2)= 25

21- (-4) = 25. Therefore this is the correct solution. 

MG
Answered by Màiri G. Maths tutor

11694 Views

See similar Maths GCSE tutors

Related Maths GCSE answers

All answers ▸

What is the cosine rule?


Given point A: (5,9), point B: (d,15) and the gradient of line AB is 3... what is the value of d?


expand (x-3)^2


How do I solve a quadratic equation by factorising?


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