a If either of the variable terms would cancel out the corresponding variable term in the other equation, you can use the Elimination Method to solve the system.
B
b Does either of the equations have an isolated variable in it?
A
a (4/3, 10)
B
b (2/3,17/3)
Practice makes perfect
a Even though both equations have a variable with a coefficient of 1, the Substitution Method may not be the easiest. Instead, we will use the Elimination Method.
To solve a system using this method, one of the variable terms needs to be eliminated when one equation is added to or subtracted from the other equation. This means that either the x-terms or the y-terms must cancel each other out.
y+3 x=14 & (I) y-3 x=6 & (II)We can see that the x-terms will eliminate each other if we add Equation (II) to Equation (I).
In this system of equations, at least one of the variables has a coefficient of 1. Therefore, we will approach its solution with the Substitution Method. When solving a system using this method, there are three steps.
Isolate a variable in one of the equations.
Substitute the expression for that variable into the other equation and solve.
Substitute this solution into one of the equations and solve for the value of the other variable. For this exercise, y is already isolated in one equation, so we can skip straight to solving!
