How do I solve 3x + y = 11 & 2x + y = 8?

In order to solve this set of simultaneous equations, we will rearrange each equation to use substitution. The aim of this problem is to find out what the value of x and y is. Let's rearrange equation 1 and make y the subject of the equation (i.e. move y to the left of the equals sign, and everything else to the right).

3x + y = 11
y = 11 - 3x

We have rearranged equation 1 so we now have an expression for y in terms of x. Let's now substitute this value of y into equation 2.

2x + y = 8
2x + (11 - 3x) = 8

We now have an equation in terms of x only, so we can go ahead and solve for x.

2x -3x = 8-11
-x = -3
x = 3

We have now obtained a value for x. Now, to find out what y is we just need to substitute it back into our equation for y.

y = 11 -3x
y = 11- 3*3
y = 11-9
y = 2

In a simultaneous equation, you can always double check your answer is correct by substituting your values of x and y into any of the equations and seeing if it holds true. Lets test this by substituting x = 3 and y = 2 into equation 2.

2x + y = 8
2*3 + 2 = 6 + 2 = 8

As these values satisfy the equation, we know that our answer is correct.

Answered by Naomi O. Maths tutor

12915 Views

See similar Maths GCSE tutors

Related Maths GCSE answers

All answers ▸

How do I work out the length of sides on a right-angle triangle?


Find the two solutions to the quadratic equation x^2-9x+18


What exactly is pi?


Find y and x of the to following equations: x +3y = 11 and x + 2y = 9.


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 2013–2024

Terms & Conditions|Privacy Policy
Cookie Preferences