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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?

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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}
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if both lines cross at one point, then it has one solution|dw:1341765726344:dw|

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Other answers:

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

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