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?

Answer 1

d

Explanation:

Answer 2

d. The cost of natural gas (y) = $0.83 per unit

Explanation:

The explanation is shown below:-

the equation of system is:

750x + 17y = 141.61 (i)

300x + 30y =75.90 (ii)

as x indicates the cost of electricity and y indicates the costs of natural gas.

we will solve the both equation with the help of multiplication for (i) by 30 and for (ii) 75

`30* (750x + 17y) 30* 141.61\\\\`

after solve the above equation we will get

22,500x + 510y = 4248.3 (iii)

`75* (330x + 30y) = 75* 75.90`

after solve the above equation we will get

22500x + 2250y = 5692.5 (iv)

After deducting the equation (iii) and (iv) we will get

1740 y = 1444.2

After Dividing by 15 both sides,

116y = 96.28

So, Katrina simplify the above system using linear equation and reach at the equation that is

116 y = 96.28

By Division property of equality defines that divide the equal no. of both sides of an equation:

by Division of 116 to both sides of an equation, to get y:

`(116y)/(116) = (96.28)/(116)`

y = 0.83

So, the natural gas is $0.83 per unit