Question

One week, Huang ordered 1 pizza and 2 sodas for $12. The next week, he ordered 3 pizzas and 4 sodas from the same restaurant for $30. Write and graph a system of equations to determine the cost of each pizza and the cost of each soda from this restaurant.
Let x = the cost of a pizza
Let y = the cost of a soda

(1) A pizza costs $8 and a soda costs $4.

(2) A pizza costs $6 and a soda costs $3.

(3) Individual costs cannot be determined. There is no solution.

(4)There are many possible costs for each. There are infinitely many solutions.

Answer 1

since x is pizza cost and y is soda cost, and we know that he bought 1x and 2y and that was 12 dollars, and he bought 3x and 4y and that was 30, we set up parallel equations.

1x+2y=12
3x+4y=30

Solve for x in the first equation

x+2y=12
Subtract 2y from both sides
x=12-2y

Now we know that x=12-2y and we substitute this in the next equation

Replace the x's with (12-2y) in the second equation.
3(12-2y)+4y=30
Use the distributive property for 3(12-2y)
36-6y+4y=30

Combine like terms
36-2y=30
Subtract 36
-2y=-6
Divide both sides by -2
y=3

We know that the cost of a soda is 3, and now we go back to find what x is.

x+2y=12
Substitute y for 3
x+(2*3)=12
Combine like terms
x+6=12
Subtract 6
x=6

We now have completed our problem. A soda costs 3 dollars and a pizza costs 6 dollars.
Hope this helped! :D

Answer 2

thank you so much :)