Question

A system of equations is given below. y = negative 2 x + one-fourth and y = negative 2 x minus one-fourth

Answer 1

Question:

A system of equations is given below.
`y = -2x + (1)/(4)` and
`y = -2x - (1)/(4)`.

What is true about both lines?

Answer:

They have the same slope but different y-intercepts, so they have no solution.

Explanation:

Given

`y = -2x + (1)/(4)`

`y = -2x - (1)/(4)`

Required

Which is true?

A linear equation is represented as:

`y = mx + b`

Where

`m = slope`

`b = y\ intercept`

For:
`y = -2x + (1)/(4)`

`m = -2`

`b = (1)/(4)`

For
`y = -2x - (1)/(4)`

`m = -2`

`b = -(1)/(4)`

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.