Solve these simultaneously to find values for a and b: 6a + b = 16 and 5a - 2b = 19

In order to tackle questions like this with two letters of unknown value, first what we try to do is eliminate one of the variables completely from an equation. If we call 6a + b = 16 eqn 1 and 5a - 2b = 19 eqn 2, we can see that if we multiply both sides of eqn 1 by 2, and add eqn 2 to the new equation we get, we can get rid of the 'b' term, making the equation in terms of 'a' only. Doing this gives us the following: (12a +2b = 32) + (5a -2b = 19), which goes on to give 17a = 51, meaning a = 3. Substituting this value for 'a' back into one of the original equations will give us the answer for 'b'. Putting a = 3 into eqn 1 gives: (6 x 3) + b = 16, which goes on to give 18 + b = 16, meaning b = -2.

Answered by Malvika P. Maths tutor

4354 Views

See similar Maths GCSE tutors

Related Maths GCSE answers

All answers ▸

3. (a) State the nth term of each of the following sequences: (i) 3, 7, 11, 15, 19, ....


The first four terms of an arithmetic sequence are : 11, 17, 23, 29. In terms of n, find an expression for the nth term of this sequence.


at a shop in the US tax is added onto the price of an item at the till. this shop adds 5.7% of the items value to the total cost. if you buy a ball priced as $15, how much will you have to pay ?


How do I solve simultaneous equations when one of the equations is not linear?


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