How do I solve the simultaneous equations 5x - 3y = -1 and 3x + y = 5?

One method of solving these is by elimination. We can try to subtract a multiple of one equation from the other to cancel the x's (or y's).

5x - 3y = -1 (A)
3x + y  = 5  (B)

In this case, we can add 3*(equation B) to equation A to cancel the y's. We get

14x = 14, so x = 1.

To find y, substitute this value of x into one of the original equations and solve for y.

5 - 3y = -1 (A, sub x = 1)
6 - 3y = 0
     3y = 6
      y  = 2

So the answer is x = 1, y = 2. It's a good idea to check your answer using the other equation (the one you didn't substitute into before).

3x + y = 5 (B)
 3  + 2 = 5 (sub x = 1, y = 2)

The last equation is clearly true, so we have in fact found the correct x and y.

Answered by Alex K. Maths tutor

11722 Views

See similar Maths GCSE tutors

Related Maths GCSE answers

All answers ▸

Write √5 ( √8 + √18 ) in the form a√10, where a is an integer, without using a calculator.


The perimeter of a right-angled triangle is 72 cm. The lengths of its sides are in the ratio 3 : 4 : 5 Work out the area of the triangle.


c) Sharon is organising an event. The tickets cost 12 pounds each. Sharon paid 200 pounds for the cost of the event. How many tickets will Sharon have to sell to make a profit? (2 marks)


The perimeter of a right angled triangle is 72cm. The length of its sides are in the ratio 3:4:5. Work out the area of the triangle.


We're here to help

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