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

4394 Views

See similar Maths GCSE tutors

Related Maths GCSE answers

All answers ▸

Factorise and solve x^2 -8x=15=0


A rectangle has an area of 20cm^2. Its length and width are each enlarged by scale factor 3. What is the area of the enlarged rectangle?


You have a list of numbers: 1, 45, 81, 40, 7, 8, 14, 23, 7, 4. Calculate the mode, median, and mean.


When rolling two dice, what is the probability of rolling 7?


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