SOLUTION: Suppose you need to solve a system of equations in which both equations represent lines. How many solutions can your system have? Select ALL that are possible. 3, 0,

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Question 352206:
Suppose you need to solve a system of equations in which both equations represent lines. How many solutions can your system have? Select ALL that are possible.
3, 0, infinitely many, 4, 1, 2
How many solutions does the following system of equations have?
-x-3y=3
x-6y= 5
Answer by sofiyac(983) About Me  (Show Source):
You can put this solution on YOUR website!
System of equations (lines) can have either no solution, 1 solution or infinitely many solutions.
-x-3y=3
x-6y= 5
Solve second equaiton for x by adding 6y to each side, so you get
a) x=5+6y. Now plug that into the first equation for x so you get
-(5+6y)-3y=3. Now distribute the minus and you get
-5-6y-3y=3. Add like terms and you get
-5-9y=3. Add 5 to each side of the equation and you get
-9y=8. Divide each side by -9 and you get
y=-8/9. Now you plug that into the equation i market with letter a).
So x=5%2B6%28-8%2F9%29=5-16%2F3=%2815-16%29%2F3=-1%2F3. Thus you have only one solution to this problem, which is the point (-1/3,-8/9). The "solution" in lenear equations means thats where the two lines intersect/cross each other.