How do you solve the following system?: $6x +5y =-1 , -5x -9y = 5$

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How do you solve the following system?: $6x +5y =-1 , -5x -9y = 5$

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Answer 1 · 2018-03-24T18:27:49

$x = 16/29$
$y = -25/29$

Explanation:

For solving using substitution method you have to separate out the value of any one variable $(x or y)$ in any of the equation and put it in the other equation.
Assuming $6x + 5y = -1$ to be equation $1$ and $-5x - 9y = 5$ be equation $2$
Seperating out the value of $x$
$x = (-1 - 5y)/6$ and now putting it in the second equation
$-5((-1-5y)/6) - 9y = 5$
$5((1+5y)/6) - 9y = 5$
$((5 + 25y)/6) - 9y = 5$
Now on taking $LCM$ on LHS
$((5 + 25y - 54y)/6) = 5$
$(5 + 25y - 54y) = 30$
$5 - 29y = 30$
$29y = -25$
$y = -25/29$
Now put the value of $y$ in any of the two equations
$(6x + 5(-25/29)) = -1$
$(6x -125/29) = -1$
$6x = 125/29 - 1$
$6x = (125-29)/29$
$6x = 96/29$
$x = 16/29$

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How do you solve the following system?: $6x +5y =-1 , -5x -9y = 5$

1 Answer

Explanation:

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