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!