Question

2x + 8y = 6
-5x - 20y = -15
options: (5,2), (2,5), infinitely many solutions, no solution

Explanation:

Step1: Simplify the second equation

Multiply the second equation by $-\frac{1}{5}$:
$$\frac{-5x -20y}{-5} = \frac{-15}{-5}$$
$$x + 4y = 3$$
Rearrange to match the first equation's form:
$$2x + 8y = 6$$

Step2: Compare the two equations

The first equation is $2x + 8y = 6$, and the simplified second equation is identical to the first. This means the two equations represent the same line, so there are infinitely many points (solutions) that satisfy both.

Answer:

Infinitely many solutions