Question

CALCULATORSiMAKING AN ARGUMENT One admission to an ice skating rink costs x dollars, and renting a pair of ice skates costs y dollars. Your friend says shecan determine the exact cost of one admission and one skate rental. Is your friend correct? Explain.DAGICE RINK1200D&G ICE RINK2 Sute RetailTools 30010 Sluit RentalsTS 190 00My friend isWrite the system of equations to represent the situation. Use x for the cost of admission and y for the cost of a skate rental.Equation for Receipt 240796:Check? Help< PREV45689NEXT6 of 21 answered

Answer 1

We can write one equation per receipt. We have two unknowns (x and y) and two equations, so if they are not a linear combination, we can calculate the value of x and y.

Receipt 240796 equation:

`3x+2y=38`

Receipt 240797

`15x+10y=190`

We can apply the substitution to solve this as:

`\begin{gathered} 3x+2y=38 \\ 3x=38-2y \\ x=(38-2y)/(3) \end{gathered}`
`\begin{gathered} 15x+10y=190 \\ 15((38-2y)/(3))+10y=190 \\ 5(38-2y)+10y=190 \\ (38-2y)+2y=38 \\ -2y+2y=38-38 \\ 0=0 \end{gathered}`

The two equations are a linear combination, so we don't have a unique solution.

The second equation is the first one multiplied by 5, so it doesn't add new information. Then we only have only one independent equation and two unknowns, so we have infinite solutions for the system.

`\begin{gathered} 5(3x+2y)=5(38) \\ 15x+10y=190 \end{gathered}`

He won't be able to calculate the individual value.

The system has infinite solutions (linear combinations for x and y).