After isolating y in both equations, which expression is shorter?
Equation to Be Manipulated: 3x-y=0 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-y=0 & (I) 2x+y=-10 & (II)
Which variable in which equation would be the easiest to isolate? Well, the coefficient of y in the equations is 1 or -1, which makes it easy to isolate y.
3x=y y= -2x-10
If we rearrange the first equation, we get the following system.
y= 3x y= -2x-10
We should also consider how difficult the substitution will become when we solve the system. The expression equal to y in (II) is more complicated than the expression equal to y in (I), so we should use (I) to solve for a variable.
