Chapter 8.3, Problem 2GP

To determine

To calculate:To find twosolutions for the below equation to find how much food can be bought with $\$9$ −

  $2x+y=9$

Answer to Problem 2GP

The two solutions are $\left(1,7\right)$ and $\left(2,5\right)$ .

This means, when $1$ burrito is bought, $7$ tacos can be bought, together costing $\$9$ .

And, when $2$ burritosare bought, $5$ tacos can be bought, together costing $\$9$ .

Explanation of Solution

Given information:

Equation is $2x+y=9$

Formula Used:

To solve an equation with multiple variables, we need to consider some random values for one of the variables and solve for the other one to find the solution.

Calculation:

Given equation is $2x+y=9$

Using the above explanation, we have -

Let the value of $x$ be $1$ , substituting the value of $x$ in the above equation, we have:

  $2\left(1\right)+y=9$

Solving the above equation, we have :

  $\begin{array}{l}2+y=9\\ y=7\end{array}$

Thus, the first solution is $\left(1,7\right)$ .

This means, when $1$ burrito is bought, $7$ tacos can be bought, together costing $\$9$ .

Using the same approach to find the other solution −

Let the value of $x$ be $2$ , substituting the value of $x$ in the above equation, we have:

  $2\left(2\right)+y=9$

Solving the above equation, we have :

  $\begin{array}{l}4+y=9\\ y=5\end{array}$

Thus, the second solution is $\left(2,5\right)$ .

This means, when $2$ burritosare bought, $5$ tacos can be bought, together costing $\$9$ .