Question

svlc algebra 1a - standard (15260)
solving systems of linear equations: linear combinations
how many solutions are there to the system of equations?
\\(\

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

\\)
options:
two solutions
one solution
an infinite number of solutions
no solutions

Explanation:

Step1: Simplify the second equation

Multiply the second equation \(-0.08x + 0.10y = 0.10\) by \(-50\) to eliminate decimals.
\((-0.08x + 0.10y) \times (-50) = 0.10 \times (-50)\)
\(4x - 5y = -5\)

Step2: Compare with the first equation

The first equation is \(4x - 5y = 5\). Now we have two equations:

1. \(4x - 5y = 5\)
2. \(4x - 5y = -5\)

These are two parallel lines (since they have the same slope and different y-intercepts, or in this case, the left - hand sides are the same and the right - hand sides are different). Parallel lines never intersect, so there are no solutions.

Answer:

no solutions