Question

how many solutions are there to the system of equations?\\\

$$\begin{cases}4x - 5y = 5\\\\-0.08x + 0.10y = 0.10\\end{cases}$$

\\\\(\bigcirc\\) no solutions\\(\bigcirc\\) one solution\\(\bigcirc\\) two solutions\\(\bigcirc\\) an infinite number of solutions

Explanation:

Step1: Simplify the second equation

Multiply the second equation by 100 to eliminate decimals:
$$-0.08x + 0.10y = 0.10 \implies -8x + 10y = 10$$
Divide the result by -2:
$$4x - 5y = -5$$

Step2: Compare the two equations

The first equation is $4x - 5y = 5$, and the simplified second equation is $4x - 5y = -5$. These are two parallel lines (same coefficients for $x$ and $y$, different constants) that never intersect.

Answer:

no solutions