Question

Solve the system by substitution: 0.25x + 0.28y = 14(0.75). What is the solution?

A) x = 20, y = 18
B) x = 12, y = 16
C) x = 18, y = 20
D) x = 16, y = 12

Answer 1

To solve the system of equations by substitution, first solve one equation for one variable in terms of the other. Then substitute this expression back into the second equation. In this case, the system has infinitely many solutions.

Step-by-step explanation:

To solve the system of equations by substitution, we need to find the value of one variable in terms of the other and then substitute it back into one of the equations. Let's solve the given system:

0.25x + 0.28y = 14(0.75)

First, solve the equation for x:

0.25x = 14(0.75) - 0.28y

0.25x = 10.5 - 0.28y

x = (10.5 - 0.28y)/0.25

Now, substitute this expression for x in the second equation:

0.25((10.5 - 0.28y)/0.25) + 0.28y = 14(0.75)

Simplify the equation:

10.5 - 0.28y + 0.28y = 10.5

10.5 = 10.5

After simplifying, we obtain the equation 10.5 = 10.5, which is true for any value of y. Therefore, the system has infinitely many solutions. The correct answer choice is not provided in the options.