Intermediate Algebra (11th edition)

Step 4 Now solve for y. From Step 1, , so if then

Let

Step 5 Check the solution in both equations (1) and (2).

CHECK (1) (2)

✓ True ✓ True

The solution set is NOW TRY

Solving a System with Fractional Coefficients

Solve the system.

(1)

(2)

This system will be easier to solve if we clear the fractions in equation (1).

Multiply (1) by the LCD, 6.

Distributive property

4 x- 3 y= 7 (3)

6 #

2

3

x- 6 #

1

2

y= 6 #

7

6

6 a

2

3

x-

1

2

yb = 6 a

7

6

b

3 x-y= 6

2

3

x-

1

2

y=

7

6

EXAMPLE 5

51 1, 5 26.

13 = 13 - 1 =- 1

3 + 10  13 4 - 5 - 1

3112 + 2152  13 4112 - 5 - 1

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

1 1, 5 2

y= 1 + 4112 = 5. x=1.

y= 1 + 4 x x=1,

214 CHAPTER 4 Systems of Linear Equations

Now the system consists of equations (2) and (3).

(2)

4 x- 3 y= 7 (3)

3 x- y= 6

To use the substitution method, we solve equation (2) for y.

(2)

Subtract 3x.

Multiply by. Rewrite.

Substitute for yin equation (3).

(3)

Let

Distributive property

Combine like terms.

Subtract 18.

x= Divide by - 5.

11

5

- 5 x=- 11

- 5 x+ 18 = 7

4 x- 9 x+ 18 = 7

4 x- 313 x- 62 = 7 y= 3 x-6.

4 x- 3 y= 7

3 x- 6

y= 3 x- 6 - 1

- y= 6 - 3 x

3 x- y= 6

Remember to

multiply each

term by 6.

This equation is equivalent

to equation (1).

Be careful

with signs.

NOW TRY
EXERCISE 4
Solve the system.

3 x- 2 y= 25

5 x+ y= 7

NOW TRY ANSWER

4. 51 3, - 826