Easy Algebra Step-by-Step

206 Easy Algebra Step-by-Step

You solve the system when you answer the question: What are the coor-

dinates of the point of intersection, if any, of the two lines? Here are three

methods for solving a system of equations.

Solving a System of Equations by Substitution

To solve a system of equations by substitution, you solve one equation for

one of the variables in terms of the other variable and then use substitution

to solve the system. (See Chapter 14 for a discussion on how to solve linear

equations.)

Problem Solve the system.

3

xy

xy+=y

Solution

Step 1. Solve the fi rst equation, 2x − y= 0, for y in terms of x.

2 x − y= 0

2 x − y+y= 0 +y

2 x=y

Step 2. Substitute 2x for y in the second equation,

x+y= 3, and solve for x.

x + ( 2 x) = 3

3 x= 3

3

3

3

3

x

=

x= 1

Step 3. Substitute 1 for x in the second equation,

x+y= 3, and solve for y.

1 +y= 3

1 +y − 1 = 3 − 1

y= 2

Step 4. Check whether x= 1 and y= 2satisfy both

equations in the system.

When you use the substitution

method, enclose substituted

values in parentheses to avoid

errors.

When you use the substitution

method, you can substitute the

value for x in either equation. Just

pick the one you think would be

easier to work with.

Always check your solution in

both equations when you solve a

system of two linear equations.