Answer
To use the substitution method, we isolate one of the variables on one side of the equation and then substitute its equivalent value into the other equation in the system and solve for the remaining variable.
Work Step by Step
To use the substitution method, we isolate one of the variables on one side of the equation and then substitute its equivalent value into the other equation in the system and solve for the remaining variable. To illustrate, let us use the following system of equations: $$y = 3 - 3x$$ $$3x + 4y = 6$$ Since we already have a variable isolated in one of the equations, it's simpler to use this one as the primary step and substitute its equivalent value into the other equation: $$3x + 4y = 6$$ $$3x + 4(3 - 3x) = 6$$ $$3x + 12 - 12x = 6$$ $$6 = 9x$$ $$\frac{2}{3} = x$$ Having found this value for $x$, we can now "plug" it into the equation with the initially isolated variable to finish the job: $$y = 3 - 3x$$ $$y = 3 - 3(\frac{2}{3})$$ $$y = 3 - 2 = 1$$
