Solve this pair of simultaneous equations: 3x + y= 7 and 3x - y = 5

Step 1: Start off by labeling the 2 equations. 3 x + y = 7 will be equation 1. 3 x - y = 5 will be equation 2.

Step 2: rearrange equation 1 to make y the subject. 3 x + y = 7 ---> y = 7 - 3 x (here 3 x is now negative as it has switched sides, in other words 3 x has been subtracted from both sides of the equation).

Step 3: rearrange equation 2 to make y the subject. 3 x - y = 5 ---> - y = 5 - 3 x ---> y = -5 + 3 x ---> y = 3 x - 5 ---> *** top tip *** keep your '=' signs in line with each other for nicer presentation and to stop you getting muddled!

so now y = 7 - 3x and y = 3 x - 5

step 4: substitution

If y = 7 - 3 x and 3 x - 5 then:

7 - 3 x = 3 x - 5.

Step 5: put all your like terms on the same side .

7 + 5 = 3 x + 3 x ---> 12 = 6x ---> (12/6) = x ---> x = 2

step 6: substitute x=2 into equation 1. y = 7 - 3x ---> y = 7 - 3(2)---> y = 7 - 6 ---> so y = 1 .

Answer: x = 2 and y = 1

Step 7 is optional but definitely worth it!!! - check your answer by substituting x = 2 into the equation 2 as well and see if you get the same answer. y = 3 x - 5 ---> y = 3(2) - 5 ---> y = 6 - 5 again y = 1 so you can be sure you have got the right answer!

AG
Answered by Anna G. Maths tutor

14344 Views

See similar Maths GCSE tutors

Related Maths GCSE answers

All answers ▸

2(y+3) = 10. What is y?


What is the fraction of blue beads?


Solve x^2 - 3x - 10 = 0 for x by a) factorising and b) the quadratic equation. Then draw a graph of the function, marking when it touches each of the axes.


Give the prime factorisation of 630


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