Question

question
determine if the following system of equations has no solutions, infinitely many solutions or exactly one solution.
$4x + 3y = -8$
$-8x - 6y = 16$

answer
○ no solutions ○ one solution
○ infinitely many solutions

Explanation:

Step1: Analyze the second equation

Take the second equation $-8x - 6y = 16$, divide all terms by $-2$.
$\frac{-8x}{-2} + \frac{-6y}{-2} = \frac{16}{-2}$ simplifies to $4x + 3y = -8$

Step2: Compare the two equations

The simplified second equation is identical to the first equation $4x + 3y = -8$. This means the two equations represent the same line, so every point on the line is a solution.

Answer:

Infinitely Many Solutions