Exercise 10 Page 230

We want to write and solve a system of linear equations to find the number of lilies and tulips in a bouquet that is made of these flowers. Let x be the number of lilies and let y be the number of tulips. We know that the bouquet has 12 flowers. This means that if we add the number of lilies and the number of tulips, we will get 12. x+y=12 We also know that lilies cost $3 each and tulips cost $2 each and that the bouquet costs $32. This means that if we multiply 3 by the number of lilies and add the number of tulips multiplied by 2, we will get the price of the whole bouquet. 3x+ 2y= 32 Now, we can combine these two equations into a system of linear equations. x+y=12 3x+2y=32 To solve this system, let's solve the first equation for x. Then we will substitute the expression for x into the second equation.

x+y=12 & (I) 3x+2y=32 & (II)

SubEqn

(I): LHS-y=RHS-y

x=12-y 3x+2y=32

Substitute

(II): x= 12-y

x=12-y 3( 12-y)+2y=32

Distr

(II): Distribute 3

x=12-y 3(12)-3(y)+2y=32

Multiply

(II): Multiply

x=12-y 36-3y+2y=32

AddTerms

(II): Add terms

x=12-y 36-y=32

AddEqn

(II): LHS+y=RHS+y

x=12-y 36=32+y

SubEqn

(II): LHS-32=RHS-32

x=12-y 4=y

RearrangeEqn

(II): Rearrange equation

x=12-y y=4

Now that we found the value of y, we can substitute it into the first equation to find x.

x=12-y y=4

Substitute

(I): y= 4

x=12- 4 y=4

SubTerm

(I): Subtract term

x=8 y=4

We found that x=8 and y=4. This means that there are 8 lilies and 4 tulips in the bouquet.