# Thread: Applications of Linear Systems

1. ## Applications of Linear Systems

I need help understanding this problem:

Tyrel and Dalia bought some pens and pencils. Tyrel bought 4 pens and 5 pencils, which cost him $6.71. Dalia bought 5 pens and 3 pencils, which cost her$7.12. Let a equal the price of a pen. Let b equal the price of a pencil.

a.Write an equation that relates the number of pens and pencils Tyrel bought and the amount he paid for them.
b.Write an equation that relates the number of pens and pencils Dalia bought and the amount she paid for them.
c.Solve the systems you wrote for parts (a) and (b) to find the price of a pen and the price of a pencil.

Thanks for helping!

2. Originally Posted by amberkraidich
I need help understanding this problem:

Tyrel and Dalia bought some pens and pencils. Tyrel bought 4 pens and 5 pencils, which cost him $6.71. Dalia bought 5 pens and 3 pencils, which cost her$7.12. Let a equal the price of a pen. Let b equal the price of a pencil.

a.Write an equation that relates the number of pens and pencils Tyrel bought and the amount he paid for them.
b.Write an equation that relates the number of pens and pencils Dalia bought and the amount she paid for them.
c.Solve the systems you wrote for parts (a) and (b) to find the price of a pen and the price of a pencil.

Thanks for helping!
Hi amber,

Let a = cost of each pen
Let b = cost of each pencil

a. 4a + 5b = 6.71

b. 5a + 3b = 7.12

c. Use elimination method to solve the system

Multiply equation a by -3.
Multiply equation b by 5.

-12a - 15b = -20.13
25a + 15b = 35.60
---------------------

Add the two equations to get:

13a = 15.47

a= 1.19

Substitute this value for a back into either equation to solve for b