Question

Classify the systems of equations based on the number of solutions they have.

4x + 10y = 40
2x + 5y = 40

Answer 1

The given system of equations is:

4x + 10y = 40
2x + 5y = 40

We can solve this system using any method such as substitution, elimination, or matrix algebra. Let's solve it using the elimination method:

Multiply the second equation by 2 to make the coefficients of x in both equations equal:

4x + 10y = 40
4x + 10y = 80

Now subtract the first equation from the second equation:

(4x + 10y) - (4x + 10y) = 80 - 40
0 = 40

This equation, 0 = 40, is not true. It implies that there is no solution to the system of equations. Therefore, the given system of equations does not have any solutions.