math question?

Question

The cost of 1 taco and 1 milk is $2.10. The cost of 2 tacos and 3 milks is $5.15.

Write an expression for the cost of two tacos.

Write an expression for the cost of three glasses of milk.

Write an equation that shows that the total cost of two tacos and three glasses of milk is $5.15. Show the system of equations you can use to solve this problem. Solve the system of equations and answer the problem.

Answer 1

taco=t
milk=m

t+m=2.10

2t+3m=5.15

solve from there

Answer 2

Tacos will be represented by x.
Milks will be reperesented by y.
The cost of two tacos is 2x.
The cost of three glasses of milk is 3y.

Your system of equations is:
x + y = 2.10 Because one taco and one milk equal $2.10.
2x + 3y = 5.15 Because two tacos and three milks equal $5.15.

You need to cancel out either the x's or the y's. I choose the x's . To do this you must multiply the top equation by 2 and the bottom one by 1. This will give you.
2 [ x + y = 2.10] ------------> 2x + 2y = 4.20
1 [ 2x + 3y = 5.15] ------------> 2x + 3y = 5.15
Now you will subtract them.
2x + 2y = 4.20
- (2x + 3y = 5.15)
The parantheses are so you will distribute the subtraction (negative sign) evenly accross all variables. When you distribute you get:
2x + 2y = 4.20
- 2x - 3y = -5.15
The 2x cancels and you are left with -y = -0.95. Divide by -1, and you get y = 0.95.
Plug in your value of y into the first equation, x + y = 2.10.
x + 0.95 = 2.10
Subtract 0.95 from both sides and you get 1.15.
x = 1.15.

This means that each taco is $1.15 and each milk is $0.95.
Check your answer by plugging in both values in either one of the equations.
x + y = 2.10 -----------> $1.15 + $0.95 = $2.10 True
2x + 3y = 5.15 -----------> 2 ($1.15) + 3 ($0.95) = 5.15 True

It checks out! Done.