Question:
A system of equations is given below. [tex]y = -2x + \frac{1}{4}[/tex] and [tex]y = -2x - \frac{1}{4}[/tex].
What is true about both lines?
Answer:
They have the same slope but different y-intercepts, so they have no solution.
Step-by-step explanation:
Given
[tex]y = -2x + \frac{1}{4}[/tex]
[tex]y = -2x - \frac{1}{4}[/tex]
Required
Which is true?
A linear equation is represented as:
[tex]y = mx + b[/tex]
Where
[tex]m = slope[/tex]
[tex]b = y\ intercept[/tex]
For: [tex]y = -2x + \frac{1}{4}[/tex]
[tex]m = -2[/tex]
[tex]b = \frac{1}{4}[/tex]
For [tex]y = -2x - \frac{1}{4}[/tex]
[tex]m = -2[/tex]
[tex]b = -\frac{1}{4}[/tex]
This implies that both equations have the same slope but different y intercept.
When two equations have the same slope but different y intercept; such system of equation has no solution.
