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mkumar441
How can you say the set of linear equations are solvable or not? For example: 2x+3y=4 x+2y=3 have a solution?. Based on what you say whether they have solution or not?
You try to solve it and see if the result is correct. In this example, you multiply the second equation by 2 making it 2x + 4y = 6 and then you subtract the new second from the first to get rid of x and get -y = -2 i.e. y = 2. You substitue this value in either equation to get x = -1 and since it checks out for both equations, then it's solvable and the solution is {-1,2}
thank you for your reply
if both lines cross at one point, then it has one solution|dw:1341765726344:dw|
if both lines do not cross, then they have no solutions|dw:1341765746321:dw|
if both lines are the same, then since they cross in many points, then they have infinitely many solutions|dw:1341765783010:dw| image they are both straight lines