Question

question
determine if the following system of equations has no solutions, infinitely many solutions or exactly one solution.
\\(5x + 6y = 4\\)
\\(10x + 12y = 18\\)

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

Explanation:

Step1: Simplify the second equation

Divide the second equation $10x + 12y = 8$ by 2:
$\frac{10x}{2} + \frac{12y}{2} = \frac{8}{2}$
Which simplifies to $5x + 6y = 4$

Step2: Compare the two equations

The first equation is $5x + 6y = 4$, and the simplified second equation is identical to the first. This means the two equations represent the same line, so every point on the line is a solution.

Answer:

Infinitely Many Solutions