Question

Emma buys 4 tacos and 7 enchiladas for 63 ideas and maya buys 8 tacos and 3 enchiladas for 71 dollars what is the cost for one enchilada

Answer 1

Hello there. To solve this question, we'll have to remember some properties about system of equations.

Say the cost for one enchilada is x and the cost for one taco is y.

From the values given in the problem, we can set the following system of equations:

`\begin{cases}7x+4y=63 \\ 3x+8y=71\end{cases}`

As we want to find the cost for one enchilada, we have to solve this system of equations for the variable x.

In order to do it, we start multiplying the first equation by a factor of (-2)

`\begin{cases}-14x-8y=-126 \\ 3x+8y=71\end{cases}`

Now, we add both equations

`\begin{gathered} -14x-8y+3x+8y=-126+71 \\ \\ -11x=-55 \end{gathered}`

Divide both sides of the equation by a factor of (-11)

`x=(-55)/(-11)=5`

Therefore, the cost for one enchilada is 5 dollars.