Question

karina uses the system of equations below to compare the monthly utility costs in july and december for electricity, x, and natural gas, y.
750x + 17y = 141.61
300x + 30y = 75.90
karina solves the system using linear combination and arrives at the equation 116y = 96.28. she then solves this equation for y. which statement explains karinas solution?
the cost of natural gas is $0.17 per unit.
the cost of natural gas is $0.20 per unit.
the cost of natural gas is $0.72 per unit.
the cost of natural gas is $0.83 per unit.

Explanation:

Step1: Solve the equation \(116y = 96.28\) for \(y\)

To find the value of \(y\), we use the formula \(y=\frac{96.28}{116}\).

Step2: Calculate the value of \(y\)

$$y=\frac{96.28}{116}= 0.83$$

Answer:

The cost of natural gas is \(\$0.83\) per unit.