SOLUTION: System of equations 3x+2y=1 2x-3y=2

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Question 19796: System of equations
3x+2y=1
2x-3y=2
Answer by xcentaur(357) About Me  (Show Source):
You can put this solution on YOUR website!
3x+2y=1.....[multiply by 2]
2x-3y=2.....[multiply by 3]


we multiply the equations to make the x variable equal
the first one becomes 3x*2=6x,and the second becomes 2x*3=6x
Then we can subtract and eliminate them
note that the equations do not change if you multiply them by a number,because you can always divide them and again get back you original equation.


6x+4y=2
6x-9y=6
subtract equation [2] from [1],


(6x+4y)-(6x-9y) = 2 - 6
6x+4y-6x+9y=-4
13y=-4
y=-4/13


Now look at eqn [2]
6x-9y=6
6x=6+9y
6x=6+9(-4/13)
6x=6%2B%28-36%2F13%29
6x=6-%2836%2F13%29
6x=%28%2813%2A6%29-36%29%2F13
6x=%2878-36%29%2F13
6x=42%2F13
x=%2842%2F13%29%2F6
x=42%2F%2813%2A6%29
x=7%2F13


x=7/13,y=-4/13


Hope this helps,
Prabhat