SOLUTION: Solve the system by graphing. 3x + y = –1 9x + 3y = –3 Please help me graph and solve this graphing system, I am not understanding how to solve these problems. Thanks

Algebra ->  Graphs -> SOLUTION: Solve the system by graphing. 3x + y = –1 9x + 3y = –3 Please help me graph and solve this graphing system, I am not understanding how to solve these problems. Thanks      Log On


   

Question 68746: Solve the system by graphing.
3x + y = –1
9x + 3y = –3
Please help me graph and solve this graphing system, I am not understanding how to solve these problems. Thanks
Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
The "solution" to a system of equations (aka simultaneous equations) is the intersection point(s) of the two curves or lines. In your case, the equations are linear therefore the graphs will be straight lines.
There are three possible outcomes when you graph these linear equations:
1) The lines will intersect. The point of intersection will yield a single solution.
2) The lines are parallel. There will be no point of intersection and thus, no solution.
3) The lines coincide (one on top of the other). In this case there will be an infinite number of solutions.
Let's look at the graphs:
1) 3x+y = -1
graph%28300%2C200%2C-5%2C5%2C-5%2C5%2C-3x-1%29
2) 9x+3y = -3
graph%28300%2C200%2C-5%2C5%2C-5%2C5%2C-3x-1%29
Well, as you can see, the two equations yield identical graphs. If these were plotted on the same sheet, the two lines would coincide (case 3) and so there are an infinite number of solutions.
The system is said to be a "consistent system" because it has at least one solution.