Question

A family has two cars. The first car has a fuel efficiency of 15 miles per gallon of gas and the second has a fuel efficiency of 25 miles per gallon of gas. During one particular week, the two cars went a combined total of 975 miles, for a total gas consumption of 55 gallons. How many gallons were consumed by each of the two cars that week?

Answer 1

15x+25y=975
x+y=55

Rearrange equation two so x is by itself.
x=-y+55

Plug the rearranged equation two into equation one.
15(-y+55)+25y=975

Evaluate the 'new' equation 1.
-15y+825+25y=975
10y+825=975
10y=150
y=15

Choose an equation to evaluate with y to get x. (i chose equation 2 because it was easier)
x+15=55

Evaluate the equation
x=55-15
x=40

So now we have x=40 and y=15

Evaluate those two terms with both equations to check the correctness.
15(40)+25(15)=975
600+375=975
975=975 (correct)

40+15=55
55=55 (correct)

Both equations are correct so the values of x and y are true.