# Method of Substitution (Four-Step Method)

Although on the test you can usually solve a system of two equations in two unknowns by merely adding or subtracting the equations, you still need to know a standard method for solving these types of systems.

The four-step method will be illustrated with the following system:

2

5

*x*+*y*= 105

*x*â€“ 2*y*= 7*Solve one of the equations for one of the variables*:

Solving the top equation for*y*yields*y*= 10 â€“ 2*x*.*Substitute the result from Step 1 into the other equation*:

Substituting*y*= 10 â€“ 2*x*into the bottom equation yields 5*x*â€“ 2(10 â€“ 2*x*) = 7.*Solve the resulting equation*:

5

*x*â€“ 2(10 â€“ 2*x*) = 75

*x*â€“ 20 + 4*x*= 79

*x*â€“ 20 = 79

*x*= 27*x*= 3

*Substitute the result from Step 3 into the equation derived in Step 1*:

Substituting*x*= 3 into*y*= 10 â€“ 2*x*yields*y*= 10 â€“ 2(3) = 10 â€“ 6 = 4.

Hence, the solution of the system of equations is the ordered pair (3, 4).