SOLUTION: this is my question: Determine whether the system has one solution,no solution, or many solutions: y=2/3x 2x-y=-4 could somebody please explain how

Algebra ->  Graphs -> SOLUTION: this is my question: Determine whether the system has one solution,no solution, or many solutions: y=2/3x 2x-y=-4 could somebody please explain how      Log On


   

Question 24428: this is my question: Determine whether the system has one solution,no solution, or many solutions: y=2/3x
2x-y=-4
could somebody please explain how to get the answer? Thank you.
Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
The first equation is ambiguous!
Is it y+=+%282%2F3%29x or y+=+2%2F3x???
Let's assume that it is the first case.
You can solve questions like this by graphing or algebraically.
Let's look at the graphic solution:
graph%28300%2C200%2C-5%2C5%2C-5%2C5%2C%282%2F3%29x%2C2x%2B4%29
The red line is y+=+%282%2F3%29x
The green line is y+=+2x%2B4 This is the 2nd equation written in terms of y.
Now solve algebraically by substitution:
1) y+=+%282%2F3%29x Substitute this equation for y in the second equation.
2) 2x-y+=+-4
2) 2x-%282%2F3%29x+=+-4 Simplify and solve for x.
%284%2F3%29x+=+-4 Multiply both sides by the multiplicative inverse of 4/3 (that's 3/4)
x+=+-3 Now substitute this value of x into either one of the two original equations and solve for y. Take the first equation, y+=+%282%2F3%29x
y+=+%282%2F3%29%28-3%29
y+=+-2
There is only one solution, it is: (-3, -2) Compare this with the intersection point of the two lines on the graph.
Now assume that the first equation is: y+=+2%2F3x and let's look at the graph:
graph%28300%2C200%2C-5%2C5%2C-5%2C5%2C2%2F%283x%29%2C2x%2B4%29
As you can see, there would be two solutions (points of intersection) in this case.