Which of the variables has the lowest coefficient next to it?
Equation to Be Manipulated: 5x-y=5 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.
5x+3y=11 & (I) 5x-y=5 & (II)
Which variable in which equation would be the easiest to isolate? Well, the coefficient of y in the second equation is - 1, which makes it easy to isolate y.
5x+3y=11 & (I) 5x-5=y & (II)
If we rearrange the second equation, we get the following system.
5x+3y=11 & (I) y= 5x-5 & (II)
We could have chosen to isolate y in the first equation. However, in the first equation, the coefficient of y is 3 and the constant is 11. The fact that we have easier, smaller numbers in the second equation makes this the best candidate.
