How do you determine whether a linear system has one solution, many solutions, or no solution when given 3x - y = -6 and x + y = 2?
One solution, (-1,3)
Although there are multiple ways one could solve this, I will begin with the algerbraic path to finding this solution. (Skip to bottom for shortcut)
We begin with two equations...
Lets first put them into
Now the second equation
Now that both are in y=mx+b format, set the equations equal to eachother.
Then solve for x.....
However there is a faster way to do this... using the process of elimination...
_______ Add these equations together
Then subsitute the x=-1 into any of the other equations to find the y value....