Intermediate Algebra (11th edition)

Thus, and giving the ordered pair Check this solution in both

equations of the original system.

CHECK (1) (2)

✓ True

✓ True

Since 1 4, 2 2 makes both equations true, the solution set is 51 4, 2 26. NOW TRY

6 = 6

8 - 2  6 4 = 4

2142 - 2  6 4  2 + 2

2 x-y= 6 x=y+ 2

x= 4 y=2, 14 , 22.

SECTION 4.1 Systems of Linear Equations in Two Variables 213

We found y.Now solve for xby substituting 2 for yin equation (2).

x=y+ 2 = 2 + 2 = 4 Write the x-value first

in the ordered pair.

NOW TRY
EXERCISE 3
Solve the system.

4 x- 3 y= 32

x= 3 + 2 y

Solving a Linear System by Substitution

Step 1 Solve one of the equations for either variable.If one of the equa-

tions has a variable term with coefficient 1 or , choose it, since

the substitution method is usually easier this way.

Step 2 Substitutefor that variable in the other equation. The result should

be an equation with just one variable.

Step 3 Solvethe equation from Step 2.

Step 4 Find the other value.Substitute the result from Step 3 into the

equation from Step 1 to find the value of the other variable.

Step 5 Checkthe ordered-pair solution in bothof the originalequations.

Then write the solution set.

- 1

Solving a System by Substitution

Solve the system.

(1)

(2)

Step 1 Solve one of the equations for either xor y. Since the coefficient of yin

equation (2) is , it is easiest to solve for yin equation (2).

(2)

Subtract 4x.

Multiply by.

Step 2 Substitute for yin equation (1).

(1)

Let.

Step 3 Solve for x.

Distributive property

Combine like terms. Subtract 2.

x= 1 Divide by 11.

11 x= 11

3 x+ 2 + 8 x= 13

3 x+ 211 + 4 x 2 = 13 y= 1 + 4 x

3 x+ 2 y= 13

1 + 4 x

y= 1 + 4 x - 1

- y=- 1 - 4 x

4 x- y=- 1

- 1

4 x- y=- 1

3 x+ 2 y= 13

EXAMPLE 4

NOW TRY ANSWER

3. 51 11, 4 26