Answer:
The system of equations to describe the situation is:
* $10x + 54 = 11y$
* $y = 11x$
To solve using substitution, we can substitute the second equation into the first equation. This gives us:
* $10x + 54 = 11(11x)$
* $10x + 54 = 121x$
* $-11x = -54$
* $x = 5$
We can then substitute this value of $x$ into the second equation to solve for $y$. This gives us:
* $y = 11(5)$
* $y = 55$
Therefore, the student council will need to sell 55 T-shirts to cover their costs. The costs will be $54 + $10(55) = $604.
Here is the solution in a table format:
| Variable | Value |
|---|---|
| $x$ | 5 |
| $y$ | 55 |
| Cost | $604 |
I hope this helps!
Explanation: