Question

Solve the following system of equations.

0.06x−0.13y=0.75
0.03x−0.07y=0.39
A. x=6.25,y=3.75
B. x=3.75,y=6.25
C. x=5.00,y=4.00
D. x=4.00,y=5.00

Answer 1

By using the elimination method, the system of equations was solved to find x = 3.75 and y = -3, which does not match any of the answer choices given, suggesting an error in the provided options.

Step-by-step explanation:

To solve the system of equations 0.06x - 0.13y = 0.75 and 0.03x - 0.07y = 0.39, we can use the method of elimination or substitution. Let's use elimination by first multiplying the second equation by 2 to match the coefficients of x:

• 2(0.03x - 0.07y) = 2(0.39)

This simplifies to 0.06x - 0.14y = 0.78. We now subtract this equation from the first equation:

• (0.06x - 0.13y) - (0.06x - 0.14y) = (0.75 - 0.78)

The x terms cancel out, leaving 0.01y = -0.03. Solving for y results in y = -3. Plugging y = -3 into one of the original equations, such as the second equation:

• 0.03x - 0.07(-3) = 0.39

Solving for x gives x = 3.75. Thus, the solution to the system of equations is x = 3.75 and y = -3, which is not one of the options given, indicating a possible error in the question or the answer choices provided.