Question

Classify each system as independent, dependent, or inconsistent -2x-2y=10 y=x-7

Answer 1

independent system

Explanation:

The first linear equation (
`-2x-2y=10`) can be written in slope y-intercept form by solving for the y variable. When it is in that form, one can easily understand its geometrical shape and distinguish if it the same, if it crosses or if it is parallel, to the second line (
`y=x-7`)

We proceed to re-write it in slope y-intercept form:

`-2x-2y=10\\-2x=10+2y\\-2x-10=2y\\y=(-2x-10)/(2) \\y=(-2)/(2) x-(10)/(2) \\y=-x-5`

Therefore it has a slope of "-1" and a y-intercept of "-5", while the second line has slope "1" and y-intercept "-7".

Therfore, they are lines that intercept at a unique point, and therefore represent an independent system.