Question

question
determine if the following system of equations has no solutions, infinitely many solutions or exactly one solution.
\\(5x + y = 9\\)
\\(15x + 3y = 27\\)
answer
no solutions \t\tone solution
infinitely many solutions

Explanation:

Step1: Simplify the second equation

Divide the second equation $15x + 3y = 27$ by 3:
$\frac{15x}{3} + \frac{3y}{3} = \frac{27}{3}$
Which simplifies to $5x + y = 9$

Step2: Compare the two equations

The first equation is $5x + y = 9$, 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