How do you solve $2x+y=0$ and $x-y=1$ using substitution?

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Answer 1 · 2016-06-16T21:49:27

$x =1/3 and y = -2/3$

Write one of the equations with a single variable as the subject.
This could be :
$y = -2x " or " x = 1 + y " or " y = x-1$

I would use the fact that both equations can be written with y as the subject.

As $y = y$ it follows that

$x - 1 = -2x$
$" "3x = 1$

$x = 1/3$

Now that we know the value of $x$ , substitute into one of the equations to find the value for $y$

$y = -2 xx 1/3 = -2/3$

Answer 2 · 2016-06-16T21:55:25

$2x+y=0.......(i)$
$x-y=1.........(ii)$

From $(ii)$ put $y=x-1$ in $(i)$ .

$2x+(x-1)=0$
$implies 3x=1$
$implies x=1/3$

Now,put $x=1/3$ in either $(i)$ or $(ii)$ to find the value of $y$ . I am going to put $x=1/3$ in $(i)$ but you can put in $(ii)$ for practice.

$2(1/3)+y=0$
$implies y=-2/3$

$Solution$ $Set={(1/3,-2/3)}$

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