Algebra Please Help! Determine whether the following system is independent, inconsistent, or dependent.?

Question

This is a system:
{y = x+7
{y = 7-x

Best answer will be selected tommorrow!

IS IT independent, inconsistent, or dependent.?

Answer 1

Add each equation.
2y = 14
y = 7
Now replace y with 7 in either one of the equations and solve for x.
7 = x + 7
x = 0
Answer: (0,7)
The system is independent (because it has exactly one solution).

Answer 2

Independent = 1 solution (the lines cross)

Dependent = infinite solutions (the lines actually are on top of each other, and are really the same equation)

Inconsistent = 0 solutions (lines are parallel, so they will have the same slope, but different y-intercept)

y = x+7
y = 7-x

If we re-write your equations so both x terms come first, we have:

y = x + 7
y = -x + 7

The slopes are different, so they are NOT the same lines, and they are NOT parallel. That leaves only the possiblility of being independent...they will cross at one point.

Now, that was easy, in a little bit, your teacher will want you to find the point that they cross at! Not too tough, but a little bit harder!

Answer 3

Independent

Answer 4

This system is independent.
The lines intersect at the point (0, 7).
Any time two lines intersect at exactly one point then they are independent.
Parallel lines would be inconsistent, and coinciding lines (lines on top of each other) are dependent.

Answer 5

Inconsistent. second equation could be rewritten y=-x+7. This wouldn't make sense, The answer could be x=0, but it wouldn't be listed as -x.

Answer 6

ok.. first.. are you able to regulate them to slope-intercept type? 3x - 4y = 8 ==> y= 3/4x -2... slope 3/4 and y-intercept of -2 .75x - y = -2 ==> y = 3/4x +2... slope 3/4 and y-intercept of +2 those 2 equations have an same slope.. subsequently they're parallel.. they are going to not in any respect bypass... so no answer.... i'd say that they are autonomous... yet... i'm not positive about that terminology.

Answer 7

It is dependent.