Item 7 three orders are placed at a pizza shop. two small pizzas, a liter of soda, and a salad cost $14; one small pizza, a liter of soda, and three salads cost $15; and three small pizzas, a liter of soda, and two salads cost $22. how much does each item cost?

For this case, the first thing we must do is define variables.

We have then:d

x: cost of each small pizza

y: cost of each liter of soda

z: cost of each salad.

We write the equation that models the problem:

From equation 3 we clear y:

Substituting in equation 2 we have:

Rewriting:

From here, we clear the value of z:

Then, we substitute the value of z and y in equation 1:

From here, we clear x:

Then, the value of z is:

Finally, the value of y is:

$ 5: cost of each small pizza

1 $: cost of each liter of soda  

3 $: cost of each salad.

x^2 + 81

we can factor this using difference of square binomials.

rewrite the equation:

x^2 - (-81)

factor:

(a^2 - b^2) = (√a^2 + √b^2)(√a^2 - √b^2)

(x^2 - (-81) = (x + √-81)(x - √-81)

we can remove the - from under the radical by multiplying it by i.

(x^2 - (-81) = (x + i√81)(x - i√81)

(x^2 - (-81) = (x + 9i)(x - 9i)

we can check our answer by using foil:

x^2 - 9ix + 9ix - 81i^2

x^2 - 81^2

i^2 = -1

x^2 + 81

oof. u are asking for t much