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Big Ideas Math Integrated I, 2016
BI
Big Ideas Math Integrated I, 2016 View details
1. Solving Systems of Linear Equations by Graphing
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Exercise 29 Page 222

The area of a rectangle is l* w and the perimeter is 2w+2l, where w and l are the width and the length, respectively.

Area: A=18x-18
Perimeter: P=6x+6
Solution to the System: (2,18)

Practice makes perfect

We can calculate the area of a rectangle by multiplying the width w by the length l. In the given diagram, we can see that w=3x-3 and l=6.

A=l * w
SubstituteII

w= 3x-3, l= 6

A= 6( 3x-3)
â–¼
Simplify right-hand side
Distr

Distribute 6

A=6(3x)-6(3)
AssociativePropMult

Associative Property of Multiplication

A=(6* 3)x-6(3)
Multiply

Multiply

A=18x-18
The perimeter is calculated using the formula P=2l+2w. Again, by substituting the known values for width and length, we can find a formula for the perimeter.

P=2l+2w
SubstituteII

w= 3x-3, l= 6

P=2( 6)+2( 3x-3)
â–¼
Simplify right-hand side
Distr

Distribute 2

P=2(6)+ 2(3x)-2(3)
AssociativePropMult

Associative Property of Multiplication

P=2(6)+ (2* 3)x-2(3)
Multiply

Multiply

P=12+6x-6
SubTerms

Subtract terms

P=6x+6

Finally, we can graph these linear equations and find their point of intersection.

The solution, or point of intersection, to this system of linear equations is (2,18). This means that the perimeter and area are both 18 when x=2.

Subchapter links expand_more
arrow_right Communicate Your Answer p.217
3
Communicate Your Answer 4 (Page 217)
arrow_right Monitoring Progress p.218-220
Monitoring Progress 1 (Page 218)
Monitoring Progress 2 (Page 218)
Monitoring Progress 3 (Page 219)
Monitoring Progress 4 (Page 219)
Monitoring Progress 5 (Page 219)
Monitoring Progress 6 (Page 220)
arrow_right Exercises p.221-222
Exercises 1 (Page 221)
Exercises 2 (Page 221)
Exercises 3 (Page 221)
Exercises 4 (Page 221)
Exercises 5 (Page 221)
Exercises 6 (Page 221)
Exercises 7 (Page 221)
Exercises 8 (Page 221)
Exercises 9 (Page 221)
Exercises 10 (Page 221)
Exercises 11 (Page 221)
Exercises 12 (Page 221)
Exercises 13 (Page 221)
Exercises 14 (Page 221)
Exercises 15 (Page 221)
Exercises 16 (Page 221)
Exercises 17 (Page 221)
Exercises 18 (Page 221)
Exercises 19 (Page 221)
Exercises 20 (Page 221)
Exercises 21 (Page 221)
Exercises 22 (Page 221)
Exercises 23 (Page 222)
Exercises 24 (Page 222)
Exercises 25 (Page 222)
Exercises 26 (Page 222)
Exercises 27 (Page 222)
Exercises 28 (Page 222)
Exercises 29 (Page 222)
Exercises 30 (Page 222)
Exercises 31 (Page 222)
Exercises 32 (Page 222)
Exercises 33 (Page 222)
Exercises 34 (Page 222)
Exercises 35 (Page 222)
Exercises 36 (Page 222)