SOLUTION: Post your 50-word response to the following: How do you know when an equation has infinitely many solutions? How do you know when an equation has no solution?

Question 269063: Post your 50-word response to the following: How do you know when an equation has infinitely many solutions? How do you know when an equation has no solution?
Answer by persian52(161) (Show Source): You can put this solution on YOUR website!
I think you mean a system of equations... A system of equations has infinitely many solutions if there are infinitely many values of x and y that make both equations true. A system of equations has no solution if there is no pair of an x-value and a y-value that make both equations true. For examples, suppose you have the system of equations y = 2x and y = x + 1. Then you can plug in 2x for y in the second equation and get 2x=x, so x=1. That means y=1+1=2. So the (x, y) pair that is a solution of this system is (1, 2). However, if you try that with the system of equations y = 2x and 2y = 4x, you can plug in 2x for y in the second equation and get 2(2x)=4x, or 4x=4x. Any value you plug in for x here is true, and each one goes with some value for y, so there are infinitely many (x, y) pairs that make this system true. (That's because these are the same line. Every point on either line is on both lines.) Now look at the system y = 2x and y = 2x+1. If you again plug in 2x for y in the second equation, you get 2x = 2x+1, or 0 = 1. Since this is a false statement, there is no (x, y) pair you could plug into this system to make both equations true at the same time. (That's because these lines are parallel. Then never intersect.)
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This question was answer before so i ll just give it out again! ☺

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