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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 19 Page 411

Subtract the equations in order to eliminate the x-variable.

Max: 13 hours
Sasha: 7 hours

Practice makes perfect

Examining the System of Linear Equations, we see that the x-variables have the same coefficients. This means that we can use the Elimination Method to solve for the number of hours that they exercise. Let's start by subtracting the second equation from the first and solving for the y-variable.

x+y=20 & (I) x-4y=-15 & (II)

(I):Subtract (II)

x+y-( x-4y)=20-( -15) x-4y=-15

(I): Distribute -1

x+y-x+4y=20+15 x-4y=-15

(I):Add and subtract terms

5y=35 x-4y=-15

(I):.LHS /5.=.RHS /5.

y=7 x-4y=-15

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

y=7 x-4y=-15

(II):y= 7

y=7 x-4( 7)=-15

(II): Multiply

y=7 x-28=-15

(II):LHS+28=RHS+28

y=7 x=13

We have found that Max exercises 13 hours and Sasha exercises 7 hours.

Subchapter links

Explore p.405-409

Elaborate p.409