Question

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?

Answer 1

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}

Answer 2

thank you for your reply

Answer 3

if both lines cross at one point, then it has one solution

Answer 4

if both lines do not cross, then they have no solutions

Answer 5

if both lines are the same, then since they cross in many points, then they have infinitely many solutions
image they are both straight lines