Beginning Algebra, 11th Edition

Using the Substitution Method

Use substitution to solve the system.

(1)

(2)

Step 1 We must solve one of the equations for either xor y. Because the coefficient

of yin equation (1) is , we avoid fractions by solving this equation for y.

(1)

Add y.

Subtract 2x.

Step 2 Now substitute for yin equation (2).

(2)

Let.

Step 3 Solve the equation from Step 2.

Distributive property

Combine like terms.

Subtract 12.

Multiply by.

Step 4 Equation (1) solved for yis. Since

Step 5 Check that is the solution.

CHECK (1) (2)

Substitute. Substitute.

✓ True ✓ True

Since both results are true, the solution set of the system is 51 2, 0 26. NOW TRY

4 = 4 10 = 10

2122  4 - 0 5122 + 3102  10

2 x= 4 - y 5 x+ 3 y= 10

12 , 02

y=- 2122 + 4 = 0.

y=- 2 x+ 4 x= 2 ,

x= 2 - 1

- x=- 2

- x+ 12 = 10

5 x- 6 x+ 12 = 10

5 x+ 31 - 2 x+ 42 = 10 y=- 2 x+ 4

5 x+ 3 y= 10

- 2 x+ 4

y=- 2 x+ 4

y+ 2 x= 4

2 x= 4 - y

- 1

5 x+ 3 y= 10

2 x= 4 - y

EXAMPLE 3

SECTION 4.2 Solving Systems of Linear Equations by Substitution 259

NOW TRY
EXERCISE 3
Use substitution to solve the
system.

4 x- 5 y=- 4

2 y=x- 2

Distribute 3 to

both- 2 xand 4.

OBJECTIVE 2 Solve special systems by substitution.Recall from Section 4.1

that systems of equations with graphs that are parallel lines have no solution. Systems

of equations with graphs that are the same line have an infinite number of solutions.

Solving an Inconsistent System by Substitution

Use substitution to solve the system.

(1)

(2)

Equation (1) is already solved for x, so substitute for xin equation (2).

(2)

Let from equation (1).

Distributive property

10 = 6 False

10 - 4 y+ 4 y= 6

215 - 2 y 2 + 4 y= 6 x= 5 - 2 y

2 x+ 4 y= 6

5 - 2 y

2 x+ 4 y= 6

x= 5 - 2 y

EXAMPLE 4

NOW TRY ANSWER

3. 51 - 6, - 426