How do solve the following linear system?: $3x-2y=2 , -6x+5y=1$ ?

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Answer 1 · 2016-02-01T10:10:55

Solve by substitution and elimination:

$3x-2y=2$

$-6x+5y=1$

We can eliminate $-6x$ from the second equation by $3x$ in the first equation if we multiply it with $2$ to get $6x$ .

$rarr2(3x-2y=2)$

$rarr=6x-4y=4$

Add both of the equations:

$rarr(-6x+5y=1)+(6x-4y=4)$

$rarr(5y=1)+(-4y=4)$

$rarry=5$

Substitute the value of $y$ to the second equation:

$rarr-6x+5(5)=1$

$rarr-6x+25=1$

$rarr-6x=1-25$

$rarr-6x=-24$

$rarrx=(-24)/-6=24/6=4$

Because, $(-n)/-m=n/m$

So, $(x,y)=(4,5)$

How do solve the following linear system?: 3x-2y=2 , -6x+5y=1 3x-2y=2 , -6x+5y=1 ?