Is this a system of equations?
4x-y=4
-4x+y=-4

Question

Is this a system of equations?
4x-y=4
-4x+y=-4

ganeshie8 · Answer

linear system of two dependent equations

littlebird · Answer

How do I find out if it has a solution?

igreen · Answer

Graph it or solve it

igreen · Answer

Multiply -1 to the 2nd equation..what do you get?

texaschic101 · Answer

A system of equations is a collection of 2 or more equations with the same set of unknowns

littlebird · Answer

In both equations, when solving for y,I got  y=4x-4
Does that mean they have no solution, or one unique solution?

igreen · Answer

$\sf (-4x + y = -4) \cdot -1 = ~ \! ?$

texaschic101 · Answer

wrong answer....do what igreen says...it will eventually make sense to you

littlebird · Answer

4x-y=4

texaschic101 · Answer

oh..I see what you did LittleBird...you see that both equations are equal...they are the same. That means they are the same line......infinite solutions

littlebird · Answer

I have another similar problem where the lines are parallel. Does that mean they have no solution?

texaschic101 · Answer

Little lesson.. (when finding out how many solutions a system of equations have)
In y = mx + b form, the slope is in the m position and the y intercept is in the b position.

(when comparing a system of equations)..
If the slope and the y intercepts are equal, then it has infinite solutions
if the slope is the same, but the y intercepts are different...parallel lines with no solutions.
if the slopes and the y intercepts are different, then it has 1 solution

littlebird · Answer

That is exactly what I needed to know! Thanks!

texaschic101 · Answer

anytime :)