Solving Using Substitution: Example 3

Solving Using Substitution

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).