You and a friend go to a local Mexican restaurant for lunch. You order 2 soft tacos and 3 burritos for a total bill of $8.85. Your friend orders 4 soft tacos and 2 burritos for a total bill of $12.70. How much does one taco cost? How
much does on burrito cost?

A soft taco costs $1.25 and a burrito costs $2.50

Step-by-step explanation:

To start to find the cost of each, you need to set up a system of equations. Start by using x for the cost of a soft taco. Then use y for the cost of a burrito. First you can compile an equation for what you paid.

3x + 3y = 11.25

Now you can do the same with your friend's purchase.

4x + 2y = 10.00

Now to solve we can use a number of different methods. We'll use elimination this time. To use that, multiply the first equation by -2 and the second equation by 3. Then line them up like this:

-6x - 6y = -22.50

12x + 6y = 30.00

Now we add them straight through to cancel the y's and solve for x.

6x = 7.50

x = 1.25

Now we know the cost of a soft taco is $1.25 and we can find the burrito cost by using the taco cost in either equation.

3x + 3y = 11.25

3(1.25) + 3y = 11.25

3.75 + 3y = 11.25

3y = 7.50

y = 2.50

So we know that a burrito costs $2.50