OBJECTIVE 3 Solve linear systems with fractions and decimals by
substitution.
SECTION 4.2 Solving Systems of Linear Equations by Substitution 261
NOW TRY
EXERCISE 6
Solve the system by the
substitution method.
16 x-^13 y=^43x+^12 y=^12Using the Substitution Method with Fractions as CoefficientsSolve the system by the substitution method.
(1)(2)Clear equation (1) of fractions by multiplying each side by 4.
Multiply by 4.Distributive property(3)Now clear equation (2) of fractions by multiplying each side by 4.
Distributive property2 x+ 3 y=- 10 (4)
4 a
1
2
xb + 4 a
3
4
yb = 4 a-
5
2
b
4 a
1
2
x+
3
4
yb = 4 a-
5
2
b
12 x+y= 8
413 x 2 + 4 a
1
4
yb = 4122
4 a 3 x+
1
4
yb = 4122
1
2
x+
3
4
y=-
5
2
3 x+
1
4
y= 2
EXAMPLE 6
Multiply by 4, the common
denominator.The given system of equations has been simplified to an equivalent system.
(3)
(4)To solve this system by substitution, solve equation (3) for y.
(3)
Subtract 12x.Now substitute this result for yin equation (4).
(4)
Let.
Distributive property
Combine like terms. Subtract 24.x= 1 Divide by 34.-
- 34 x=- 34
2 x- 36 x+ 24 =- 10
2 x+ 31 - 12 x+ 82 =- 10 y=- 12 x+ 8
2 x+ 3 y=- 10
y=- 12 x+ 8
12 x+ y= 8
2 x+ 3 y=- 10
12 x+ y= 8
Distribute 3 to
both- 12 xand 8.Since equation (3) solved for yis , substitute 1 for xto get
Check by substituting 1 for xand for yin both of the original equations. The
solution set is 51 1, - 426. NOW TRY
- 4
y=- 12112 + 8 = - 4.
y=- 12 x+ 8
NOW TRY ANSWER
- 51 2, - 326