Solve for x and y:

2x + 3y = 0, 3x + 4y = 5.

We have,

2x + 3y = 0 …eq.1


3x + 4y = 5 …eq.2


To solve these equations, we need to make one of the variables (in both the equations) have same coefficient.


Lets, multiply eq.1 by 3 and eq.2 by 2, so that variable x in both the equations have same coefficient.


Recalling equations 1 & 2,


2x + 3y = 0 [×3


3x + 4y = 5 [×2


6x + 9y = 0


6x + 8y = 10


On solving the two equations we get,


y = - 10


Substitute y = - 10 in eq.1/eq.2, as per convenience of solving.


Thus, substituting in eq.1, we get


2x + 3( - 10) = 0


2x = 30


x = 15


Hence, we have x = 15 and y = - 10.


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