Avehicle uses 1 1/8 gallons of gasoline to travel 13 1/2 miles. at this rate, how many miles can the vehicle travel per gallon of gasoline?

The rate is 12 miles per gallon.

Step-by-step explanation:

The vehicle uses 1 1/8 gallons of gasoline to travel 13 1/2 miles.

\implies 1\frac{1}{8}\text{ gallon of gasoline}=13\frac{1}{2}\text{ miles}

\frac{9}{8}\text{ gallon of gasoline}=\frac{27}{2}\text{ miles}

1 \text{ gallon of gasoline}= \frac{8\times 27}{9\times 2}\text{ miles}

1 \text{ gallon of gasoline}= \frac{216}{18}\text{ miles}

1 \text{ gallon of gasoline}= 12\text{ miles}

Hence, the vehicle can travel 12 miles with one gallon of gasoline,

⇒ The rate of travelling is 12 miles per gallon.

18

step-by-step explanation:

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{x = -1/2 ,   y = -1

step-by-step explanation:

solve the following system:

{2 x + y = -2

{10 x - 3 y = -2

in the first equation, look to solve for y:

{2 x + y = -2

{10 x - 3 y = -2

subtract 2 x from both sides:

{y = -2 x - 2

{10 x - 3 y = -2

substitute y = -2 x - 2 into the second equation:

{y = -2 x - 2

{10 x - 3 (-2 x - 2) = -2

10 x - 3 (-2 x - 2) = (6 x + 6) + 10 x = 16 x + 6:

{y = -2 x - 2

{16 x + 6 = -2

in the second equation, look to solve for x:

{y = -2 x - 2

{16 x + 6 = -2

subtract 6 from both sides:

{y = -2 x - 2

{16 x = -8

divide both sides by 16:

{y = -2 x - 2

{x = -1/2

substitute x = -1/2 into the first equation:

{y = -1

{x = -1/2

collect results in alphabetical order:

answer:   {x = -1/2 ,   y = -1