Question

question
determine if the following system of equations has no solutions, infinitely many solutions or exactly one solution.
\\(5x + 4y = 4\\)
\\(-10x - 8y = -8\\)

answer
\\(\circ\\) one solution \\(\circ\\) no solutions
\\(\circ\\) infinitely many solutions

Explanation:

Step1: Analyze the second equation

Notice that the second equation $-10x - 8y = -8$ can be simplified by dividing every term by $-2$.
$\frac{-10x}{-2} + \frac{-8y}{-2} = \frac{-8}{-2}$

Step2: Simplify the second equation

After division, the second equation becomes identical to the first equation.
$5x + 4y = 4$

Step3: Interpret the result

Since both equations represent the same line, every point on the line is a solution, meaning there are infinitely many solutions.

Answer:

Infinitely Many Solutions