How can you isolate the variables in the second equation? Which option will make the Substitution Method easier?
Equation to Be Manipulated: x+y=8 Variable to Be Isolated: y
Practice makes perfect
To solve a system of equations using the Substitution Method, a variable must be isolated on one side of one of the equations. Looking at the given equations, we see that it will be necessary to apply the Properties of Equality for this to happen with either equation.
3x-2y=19 & (I) x+y=8 & (II)
Notice that the coefficients of both x and y in the second equation are equal to 1, which makes it equally easy to isolate either of those variables. However, we should also consider how difficult the substitution will become when we solve the system. If we choose to isolate x in the second equation, we will have to perform the following substitution.
3( 8-y)-2y=19 & (I) x= 8-y & (II)
Conversely, if we choose to isolate y in the second equation, we will have to perform the substitution below.
3x-2( 8-x)=19 & (I) y= 8-x & (II)
Both of those methods would require us to use the Distributive Property. However, in the first case, we would have to distribute 3 to the terms in parentheses, whereas in the second case, we would have to distribute 2. Therefore, we should choose the second option and isolate y in the second equation, so that we do not have to deal with bigger numbers.
