Answer: Elimination method and substitution method are both non-graphical methods of solving simultaneous linear equations. The difference is explained below.
Step-by-step explanation: When you have two linear algebraic equations with two variables (unknowns), you will have to apply either the graphical method, the elimination method or the substitution method to arrive at the value for the two unknowns.
SUBSTITUTION METHOD: In either of both equations, one of the variables/unknowns will have a coefficient that is equal to 1. That coefficient would be made the subject of the formular. For example, in the equation x + 2y = 11, you can rewrite and make x the subject as follows;
x = 11 - 2y. With this you can go to the other linear equation and substitute for x. So if equation II is 4x - 2y = 4, substituting the value of x can now be expressed as 4(11 - 2y) - 2y = 4.
ELIMINATION METHOD: In the elimination method, the aim is to entirely remove one of the unknowns which would eventually make it easier to calculate be other unknown. However, it is important to note that this method is most effective when neither of the coefficients is equal to 1. The coefficient of either of the two variables will be made the same in both equations and by subtracting one from the other, it would be eliminated. For example, when you have
2x + 4y = 26 equation I
5x - 2y = 10 equation II
In order to eliminate x, you multiply equation I by 5 and multiply equation II by 2. You now arrive at
10x + 20y = 130 equation III
10x - 4y = 20 equation IV
By the time you subtract equation IV from equation III, 10x is eliminated and that way, you get rid of the x and solve for y.
Whatever value you calculate for y can now be substituted in either of the equations (I or II) and you get the value of x.
