How do solve the following linear system?: $- 2 x + 3 y = - 19, x - 3 y = - 6$ $-2x + 3y = -19 , x - 3y = -6$ ?

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Answer 1 · 2018-03-29T16:54:55

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$- 2 x + 3 y = - 19$ $-2x+3y=-19$
$x - 3 y = - 6$ $x-3y=-6$

We can use three methods to resolve. In this case we will use substitution

Express $x$ $x$ in second equation $x = - 6 + 3 y$ $x=-6+3y$ . Now make the substitution in the first one

$- 2 (- 6 + 3 y) + 3 y = - 19$ $-2(-6+3y)+3y=-19$ . Lets operate and transpose terms

$12 - 6 y + 3 y = - 19$ $12-6y+3y=-19$ ;

$- 3 y = - 19 - 12 = - 21$ $-3y=-19-12=-21$ . Then $y = - \frac{21}{- 3} = 7$ $y=-21/-3=7$

Now lets find $x$ $x$ from the expresion $x = - 6 + 3 y = - 6 + 21 = 15$ $x=-6+3y=-6+21=15$

The solution is $x = 15$ $x=15$ and $y = 7$ $y=7$

How do solve the following linear system?: −2x+3y=−19,x−3y=−6-2x + 3y = -19 , x - 3y = -6 ?