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?

1 Answer
Apr 17, 2018

One solution, (-1,3)

Explanation:

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...
3x-y =-6 and
x+y=2
Lets first put them into y=mx +b format
1)3x-y =-6 Given
2)-y =-6- 3x Subtraction property of Equality
3) y=6+3x Multiply both side by -1 to turn y positive
4)y=3x+6 Commutative Property
Now the second equation
1)x+y=2 Given
2)y=-x+2 Subtract x from both sides.
Now that both are in y=mx+b format, set the equations equal to eachother.
y=-x+2=3x+6
-x+2=3x+6
Then solve for x.....
However there is a faster way to do this... using the process of elimination...
3x-y =-6
x+y=2
_______ Add these equations together
4x=-4
x=-1
Then subsitute the x=-1 into any of the other equations to find the y value....