How many solutions are there to the system of equations? {-4x - 5y = 5 - 0.08x + 0.10y = 0.10} A) no solutions B) one solution C) two solutions D) an infinite number of solutions

The equations are not linearly independent, i. e. one equation cannot be transformed into the other by a simple numerical factor, so the system has exactly one solution.

Note:

equations are

-4x-5y=5 ... (1)

-0.08x+0.10y=0.10 ... (2)

If we attempt to multiply (2) by 50 to match the first coefficient:

50 (2) = >

50 (-0.08x+0.10y=0.10) = >

-4x+5y=5 ... (2a)

Since (2a) is not identical to (1), so we cannot transform (2) to (1) or vice versa by a simple numerical factor, hence the two equations are independent.