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Houghton Mifflin Harcourt Algebra 1, 2015

HM

Houghton Mifflin Harcourt Algebra 1, 2015 View details

3. Solving Linear Systems by Adding or Subtracting

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Exercise 17 Page 410

Add the equations in order to eliminate the w-variable.

Length: 48 ft
Width: 12 ft

Practice makes perfect

Examining the System of Linear Equations, we see that the w-variables have opposite coefficients. This means that we can use the Elimination Method to solve for the length and width. Let's start by adding the second equation to the first and solving for the l-variable.

2l+2w=120 & (I) l-2w=24 & (II)

(I):Add (II)

2l+2w+( l-2w)=120+ 24 l-2w=24

(I): Remove parentheses

2l+2w+l-2w=120+24 l-2w=24

(I):Add and subtract terms

3l=144 l-2w=24

(I):.LHS /3.=.RHS /3.

l=48 l-2w=24

Now that we have solved for the l-variable, we can substitute this value into the second equation and solve for w.

l=48 l-2w=24

(II):l= 48

l=48 48-2w=24

(II):LHS-48=RHS-48

l=48 -2w=-24

(II):.LHS /(-2).=.RHS /(-2).

l=48 w=12

We have found that the length of the garden is 48 feet and the width is 12 feet.

Subchapter links

Explore p.405-409

Elaborate p.409