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Anon25 [30]
3 years ago
8

Karina uses the system of equations below to compare the monthly utility costs in July and December for electricity, x, and natu

ral 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?
Mathematics
1 answer:
fiasKO [112]3 years ago
7 0

Answer:

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

Step-by-step 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\times (750x  + 17y) 30\times 141.61\\\\

after solve the above equation we will get

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

75\times (330x + 30y) = 75\times 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:

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

y = 0.83

So, the natural gas is $0.83 per unit

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