In these equations it is simplest to eliminate We do this by making the coefficients of the same y. y in both equations. This can be achieved by multiplying equation by 2, so that both equations contain 2y: 3x + 2y = 8 10x + 2y = 22 2× = To eliminate the terms, we subtract equation from equation . We get: 7x = 14 y i.e. = 2 x To find y, we substitute = 2 into one of the original equations. For example if we put it into : x 10 + = 11 y = 1 y Therefore the solution is = 2, = 1. x y Remember: You can check your solutions by substituting both x and y into the original equations. Example: Solve 2x + 5y = 16 3x 4y = 1 – Solution: We begin by getting the same number of or appearing in both equation. We can get x y 20y in both equations if we multiply the top equation by 4 and the bottom equation by 5: 8x + 20y = 64 15x 20y = 5 – As the signs in front of 20y are different, we can eliminate the terms from the equations by y ADDING: 23x = 69 + i.e. = 3 x Substituting this into equation gives: 6 + 5y = 16 5y = 10 = 2 y So… The solution is = 3, = 2. x y If you need more help on solving simultaneous equations, you can download a booklet from the following website: Exercise: Solve the pairs of simultaneous equations in the following questions: 1) + 2y = 7 2) + 3y = 0 x x 3x + 2y = 9 3x + 2y = -7
In these equations it is simplest to eliminate y. We do this by making the coefficients of y the same in both equations. This can be achieved by multiplying equation by 2, so that both equations contain 2y: 3x + 2y = 8 10x + 2y = 22 2× = To eliminate the y terms, we subtract equation from equation . We get: 7x = 14 i.e. x = 2 To find y, we substitute x = 2 into one of the original equations. For example if we put it into : 10 + y = 11 y = 1 Therefore the solution is x = 2, y = 1. Remember: You can check your solutions by substituting both x and y into the original equations. Example: Solve 2x + 5y = 16 3x – 4y = 1 Solution: We begin by getting the same number of x or y appearing in both equation. We can get 20y in both equations if we multiply the top equation by 4 and the bottom equation by 5: 8x + 20y = 64 15x – 20y = 5 As the signs in front of 20y are different, we can eliminate the y terms from the equations by ADDING: 23x = 69 + i.e. x = 3 Substituting this into equation gives: 6 + 5y = 16 5y = 10 So… y = 2 The solution is x = 3, y = 2. If you need more help on solving simultaneous equations, you can download a booklet from the following website: Exercise: Solve the pairs of simultaneous equations in the following questions: 1) x + 2y = 7 2) x + 3y = 0 3x + 2y = 9 3x + 2y = -7