Question

determine if the following system of equations has no solutions, infinitely many solutions or exactly one solution.
\\(-2x + y = 5\\)
\\(2x - y = -5\\)
answer
no solutions
infinitely many solutions
one solution

Explanation:

Step1: Analyze the two equations

First equation: $-2x + y = 5$
Second equation: $2x - y = -5$

Step2: Manipulate the second equation

Multiply the second equation by $-1$:
$-(2x - y) = -(-5)$
$-2x + y = 5$

Step3: Compare the two equations

The manipulated second equation is identical to the first equation, meaning they represent the same line.

Answer:

Infinitely Many Solutions