Solve this pair of simultaneous equations (1) 5x+2y=20 and (2) x+4y=13

To solve these equations, our aim is to find a value of x and a value of y that satisfy both equations at the same time. By satisfy we mean, if we plug our values in for x and y then the left hand side and right hand side of each equation will equal eachother.

First to find x and y we must try and eliminate either x or y to find the other.

Lets try and eliminate x.

We can write equation (2) with x as the subject by subtracting 4y from both sides, like so:

x=13-4y

Now we can substitute this into equation (1) to eliminate x giving:

5(13-4y) + 2y = 20

Expanding the brackets gives

65 - 20y + 2y = 20

Now we collect all the y's onto one side and the constants onto the other giving:

45 = 18y

Then divide through by 18 to give y=5/2

Now we substitute this into either equation (1) or (2) for y to find x.

With (1) : 5x + 2(5/2) = 20, 5x = 15, x=3

With (2) : x + 4(5/2) = 13, 5x=15, x=3

So our solution is x=3, y=5/2. It isn't necessary to show x's value with both equations but it can be useful to check your answer is correct!

JH
Answered by Jenny H. Maths tutor

3893 Views

See similar Maths GCSE tutors

Related Maths GCSE answers

All answers ▸

I have £300 I want to split between my daughters Megan, Danni and laura in the ratio 3:4:1 respectively. How much money will Danni get?


i) The point A on a graph is (6,-7), and point B is (3,5). Calculate the equation of the straight line that passes through both A and B. ii) Does the line pass through the point C (-2,26)?


How do I find roots of a quadratic equation when I can't factorise?


How do I solve simultaneous equations when one is quadratic? For example 3x^2 -2y = 19, 6x-y-14=0


We're here to help

contact us iconContact usWhatsapp logoMessage us on Whatsapptelephone icon+44 (0) 203 773 6020
Facebook logoInstagram logoLinkedIn logo

© MyTutorWeb Ltd 2013–2025

Terms & Conditions|Privacy Policy
Cookie Preferences