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 Karina’s 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.

Answer 1

Answer:

The cost of natural gas is $0.83 per unit.

Step-by-step explanation:

x = electricity

y = natural gas

karina use 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              ..........................(1)

300x + 30y = 75.90          ...........................(2)

now solve these equations.

multiply the  equation (1) with 2 and subtract it from equation (2) with multiplication of 5

  1500x + 150y = 379.5

-(1500x + 34y   = 283.22

................................................

               116y = 96.28

                  y = 96.28/116

                  y = 0.83

so,

The cost of natural gas is $0.83 per unit.