Solve each system by the elimination method. (Hint: In Exercises 29–34, first clear all frac-tions or decimals.) Check each solution. See Examples 3–5.*
Solving Special Systems Using the Elimination MethodSolve each system by the elimination method.
(a) (1)
(2)Multiply each side of equation (1) by. Then add the two equations.
Multiply equation (1) by.
(2)
FalseThe false statement indicates that the given system has solution set
(b) (1)
(2)Multiply each side of equation (1) by 3. Then add the two equations.
Multiply equation (1) by 3.
(2)
TrueA true statement occurs when the equations are equivalent. This indicates that every
solution of one equation is also a solution of the other. The solution set is
51 x, y 2 | 3 x- y= 46. NOW TRY
0 = 0
-^9 x+^3 y=-^12
9 x- 3 y= 12
- 9 x+ 3 y=- 12
3 x- y= 4
0 =- 19 0.
0 =- 19
4 x+^8 y=-^9
- 4 x- 8 y=- 10 - 2
- 2
4 x+ 8 y=- 9
2 x+ 4 y= 5
EXAMPLE 5
268 CHAPTER 4 Systems of Linear Equations and Inequalities
NOW TRY
EXERCISE 5
Solve each system by the
elimination method.
(a)
(b)
- 4 x- 3 y=- 1
4 x+ 3 y= 05 x- 5 y= 10x-y= 2NOW TRY ANSWERS
- (a)
(b) 0
51 x, y 2 |x-y= 26Complete solution available
on the Video Resources on DVD
4.3 EXERCISES
Concept Check Answertrueorfalsefor each statement. If false, tell why.
1.If the elimination method leads to the solution set of the system is
2.A system that includes the equation cannot have as a solution.Solve each system by the elimination method. Check each solution. See Examples 1 and 2.5 x- 4 y= 0 1 4, - 520 =-1, 51 0, - 126.
3. 4. 5.
x-y= 22 x+y=- 5
x-y=- 6x+y= 10
x+y= 10x-y=- 26. 7. 8.
- 5 x+ 2 y= 0
5 x=y+ 5- 3 x-y= 3
2 y=- 3 x- x-y= 10
2 x+y=- 159. 10.
- 6 x+ 3 y= 15
y= 9 - 6 x
5 y= 17 + 6 x6 x-y=- 111. 12. 13.
3 x+ 5 y= 20x+ 4 y= 16- 3 x+ 2 y=- 19
x+ y= 3
3 x+ 2 y=- 32 x- y= 12*The authors thank Mitchel Levy of Broward College for his suggestions for this group of exercises.OBJECTIVE 4 Solve special systems by elimination.
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