After isolating x in both equations, which expression is shorter?
Equation: x-2y=0 Variable: x
Practice makes perfect
To solve a system of equations by using the Substitution Method, a variable must be isolated on one side of one of the equations. Looking at the given equations, we can see that it will be necessary to apply the Properties of Equality in order to isolate a variable in either equation.
x+4y=30 & (I) x-2y=0 & (II)
Which variable in which equation would be the easiest to isolate? Well, the coefficient of x in both equations is 1, which makes it easy to isolate x in both.
x= 30-4y & (I) x= 2y & (II)
We should also consider how difficult the substitution would become when we solve the system. The expression equal to x in Equation (I) is more complicated than the expression equal to x in Equation (II), so we should use Equation (II) to solve for a variable.
