Solve each system by substitution. Then graph both lines in the standard viewing window of a
graphing calculator, and use the intersection feature to support your answer. See the Connec-
tions box in Section 4.1.( In Exercises 41 and 42, solve each equation for y before graphing.)264 CHAPTER 4 Systems of Linear Equations and Inequalities
37. 38. 39.
y=15
2
x-5
2
y=-4
3
x+19
y=- 3 x- 11 3y= 4 x- 4
y= 2 xy= 6 - x40. 41. 42.
3 x+ 3 y= 46 x+ 5 y= 13
2 x+ 3 y= 14 x+ 5 y= 5y=25
3
x-65
3
y=-15
2
x+ 10Simplify. See Section 1.8.
- 1 - x+ 7 y 2 + 13 y+x 2 46. 13 x- 4 y 2 + 14 y- 3 x 2
114 x- 3 y 2 + 12 x+ 3 y 2 1 - 6 x+ 8 y 2 + 16 x+ 2 y 2PREVIEW EXERCISES
47.What must be added to to get a sum
of 0?48.What must be added to 6yto get a sum
of 0?- 4 x
49.What must 4ybe multiplied by so that
when the product is added to 8y,the sum
is 0?50.What must be multiplied by so that
when the product is added to x, the
result is 0?- 12
- 3 x
OBJECTIVES OBJECTIVE 1 Solve linear systems by elimination. Recall that adding the
same quantity to each side of an equation results in equal sums.
If then
We can take this addition a step further. Adding equalquantities, rather than the same
quantity, to each side of an equation also results in equal sums.
If and then
Using the addition property of equality to solve systems is called the elimination
method.
Using the Elimination MethodUse the elimination method to solve the system.
(1)
(2)Each equation in this system is a statement of equality, so the sum of the right sides
equals the sum of the left sides. Adding vertically in this way gives the following.
(1)
(2)x= 4 Divide by 2.
2 x = 8
x-y= 3
x+y= 5
x- y= 3
x+ y= 5
EXAMPLE 1
AB CD, ACBD.
AB, ACBC.
Solving Systems of Linear Equations by Elimination
4.3
1 Solve linear systems
by elimination.
2 Multiply when using
the elimination
method.
3 Use an alternative
method to find the
second value in a
solution.
4 Solve special
systems by
elimination.Add left sides and add right sides.http://www.ebook777.com
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