Question

{y=x−4y=−x+6
What is the solution for this system of equations?

Answer 1

One second, please. :D

Answer 2

Okidokie! So, you are already seemingly given two equations. y=x-4 and y=-x+6 (Unless I am separating them incorrectly.) The way I love to solve these is by setting them equal to each other. The way you do this is you set them both equal to y. Then, by the recursive rule (I think) you can set them equal to each other since they = the same variable. The next step is to simplify so that you have isolated the x, and no coefficient, on one side. Hope this helps!

Answer 3

@n32carrillo

Answer 4

just making sure if that is not the case

as it might be
\[\begin{cases} y=x−4\\ y=−x+6 \end{cases}\]
or
\[\begin{cases} y=x\\ -4y=−x+6 \end{cases}\]
for either of them the way you work it out is the same -- just substitute their values in

respectively it would be:
\[\begin{cases} y=\color{lightskyblue}{x−4}\\ \color{lightskyblue}{y}=−x+6 \end{cases} \Rightarrow x-4 =-x+6 \ \ \ \ \text{ simple math from here} \]
and if the case would be the 2nd one you get:
\[\begin{cases} y=\color{slateblue}{x}\\ -4\color{slateblue}{y}=−x+6 \end{cases} \Rightarrow -4x=-x+6 \]
just solve for x