Suppose that the weight (in pounds) of an airplane is a linear function of the amount of fuel (in gallons) in its tank. When carrying 12 gallons of fuel, the airplane weighs 2078 pounds. When carrying 40 gallons of fuel, it weighs 2260 pounds. How much does the airplane weigh if it is carrying 54 gallons of fuel?

Step-by-step explanation:

GIVEN: Suppose that the weight (in pounds) of an airplane is a linear function of the amount of fuel (in gallons) in its tank. When carrying gallons of fuel, the airplane weighs pounds. When carrying gallons of fuel, it weighs pounds.

TO FIND: How much does the airplane weigh if it is carrying gallons of fuel.

SOLUTION:

Let the fuel be represented along and weight of plane along

two coordinates are

now, equation of linear function is

putting values we get

Now when fuel is

Airplane weighs

step-by-step explanation: yes

arrange the equations with like terms in columns.

analyze the coefficients of x or y.

add the equations and solve for the remaining variable.

substitute the value into either equation and solve.

check the solution.

step-by-step explanation: