Exercise 19 Page 411

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)

SysEqnSub

(I):Subtract (II)

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

Distr

(I): Distribute -1

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

AddSubTerms

(I):Add and subtract terms

5y=35 x-4y=-15

DivEqn

(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

Substitute

(II):y= 7

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

Multiply

(II): Multiply

y=7 x-28=-15

AddEqn

(II):LHS+28=RHS+28

y=7 x=13

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