Solving Using Substitution
Substitution
Example 3
Solve the system
2x + 3y = 6
-4x + y = 2
Step 1. Isolate one variable in one equation.
Since the y in the second equation has a coefficient of one, it is the easiest to isolate.
-4x + 4x + y = 2 + 4x
y = 2 + 4x
Step 2. Substitute the isolated variable's equivalent expression into the other equation.
Since y is equal to 4x + 2, substitute the "y" in 2x + 3y = 6, with the equivalent expression, 4x +2.
2x + 3(4x + 2) = 6
Step 3. Solve the remaining equation.
2x + 12x + 6 = 6
14x + 6 = 6
14x = 0
x = 0
Step 4. Substitute the value of the variable found in step 3, into either equation to find the other variable.
y = 2 + 4(0)
y = 2
Therefore, the solution point is (0, 2).