Question 19796
3x+2y=1.....[multiply by 2]
2x-3y=2.....[multiply by 3]
<P>
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.
<P>
6x+4y=2
6x-9y=6
subtract equation [2] from [1],
<br>
(6x+4y)-(6x-9y) = 2 - 6
6x+4y-6x+9y=-4
13y=-4
y=-4/13
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Now look at eqn [2]
6x-9y=6
6x=6+9y
6x=6+9(-4/13)
{{{6x=6+(-36/13)}}}
{{{6x=6-(36/13)}}}
{{{6x=((13*6)-36)/13}}}
{{{6x=(78-36)/13}}}
{{{6x=42/13}}}
{{{x=(42/13)/6}}}
{{{x=42/(13*6)}}}
{{{x=7/13}}}
<br>
x=7/13,y=-4/13
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Hope this helps,
Prabhat