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