Solve the simultaneous equations (1) x + 3y = 7 and (2) 2x + y = 4

It's impossible to solve an equation with two unknowns (x and y) so we must find a way to get rid of either x or y before solving an equation. Using substitution rearrange the equation 1 so x is the only term on one side of the equation by subtracting 3y from both sides leaving: x = 7 - 3y. Substitute that into the second equation to get 2(7 - 3y) + y = 4 Expand the brackets 14 -5y = 4 which rearranges to 5y = 10 so y = 2 Substitute y = 2 back into equation 2 to get 2x + 2 = 4 which gives x = 1 Using elimination multiply equation (1) by 2: 2x + 6y =14. Both equations now contain 2 lots of x Subtract equation 2 from equation 1 to eliminate x 5y = 10 so y = 2 Substitute y = 2 into equation 2 2x + 2 = 4 so x = 1

Answered by Simon S. Maths tutor

3665 Views

See similar Maths GCSE tutors

Related Maths GCSE answers

All answers ▸

Factorise fully y=x^2+x-12 and hence find the roots of the curve


What is the easiest way to solve a simultaneous equation?


Anna has 6 bananas. Ben has 2.5 times more bananas than Anna. Callum has a third as many bananas as Anna and Ben have together. How many bananas do Anna, Ben and Callum have together?


Emily bought 3 books and 2 apples, and she spent £19, while her brother, John, spent £15 on 1 book and 5 apples. What is the cost of one book and one apple?


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