Beginning Algebra, 11th Edition

Using the Substitution Method with Decimals as Coefficients

Solve the system by the substitution method.

(1)

(2)

Clear each equation of decimals by multiplying by 10.

Multiply equation (1) by 10.

Distributive property

(3)

Multiply equation (2) by 10.

Distributive property

- x+ 15 y= 51 (4)

101 - 0.1x 2 + 101 1.5y 2 = 101 5.1 2

101 - 0.1x+1.5y 2 = 101 5.1 2

5 x+ 24 y= 42

101 0.5x 2 + 101 2.4y 2 = 101 4.2 2

101 0.5x+2.4y 2 = 101 4.2 2

- 0.1x+1.5y=5.1

0.5x+2.4y=4.2

EXAMPLE 7

262 CHAPTER 4 Systems of Linear Equations and Inequalities

NOW TRY
EXERCISE 7
Solve the system by the
substitution method.

0.3x-0.1y=1.3

0.2x+0.3y=0.5

101 - 0.1x 2 =- 1 x=-x

Now solve the equivalent system of equations by substitution.

(3)

(4)

Equation (4) can be solved for x.

Equation (4) solved for x

Substitute this result for xin equation (3).

(3)

Let.

Distributive property

Combine like terms. Add 255.

Divide by 99.

Since equation (4) solved for xis substitute 3 for yto get

Check in both of the original equations. The solution set is

NOW TRY

1 - 6, 3 2 51 - 6, 3 26.

x= 15132 - 51 = - 6.

x= 15 y-51,

y= 3

99 y= 297

75 y- 255 + 24 y= 42

5115 y- 512 + 24 y= 42 x= 15 y- 51

5 x+ 24 y= 42

x= 15 y- 51

- x+ 15 y= 51

5 x+ 24 y= 42

NOW TRY ANSWER

7. 51 4, - 126

Complete solution available
on the Video Resources on DVD

4.2 EXERCISES

1.Concept Check A student solves the following system and finds that , which is

correct. The student gives the solution set as. WHAT WENT WRONG?

2.Concept Check A student solves the following system and obtains the equation.

The student gives the solution set as. WHAT WENT WRONG?

2 x+ 2 y= 8

x+ y= 4

51 0, 0 26

0 = 0

7 x+y= 21

5 x-y= 15

536

x= 3

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