Question

Determine if the following system of equations has no solutions, infinitely many solutions or exactly one solution.

x+4y=1
2x+8y=2

Answer 1

• Infinitely many solutions

Explanation:

First, let's organize the equations of the lines into slope-intercept form.

• x + 4y = 1
• => 4y = -x + 1
• => y = -x/4 + 1/4

And,

• 2x + 8y = 2
• => 8y = -2x + 2
• => y = -2x/8 + 2/8
• => y = -x/4 + 1/4

Since both the graphs are the same, the two equations have infinitely many solutions.