How do you find the solution of the system of equations $x-2y=2$ and $y= -1/2x-5$ ?

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Answer 1 · 2018-06-15T07:37:27

$x = -4$
$y = -3$

The second equation gives an expression for $y$ in terms of $x$ :

$y = -1/2x - 5$

This means that we can substitute the $y$ in the first equation with that expression:

$x-2color(red)(y)=2 \to x-2\color(red)((-1/2x - 5))=2$

Rearrange this last expression:

$x+x+10=2 \to 2x+10=2$

Subtract $10$ from both sides:

$2x = -8$

Divide both sides by $2$ :

$x = -4$

Now that we know $x$ , we can use the expression for $y$ to find it out:

$y = -1/2\color(red)(x) - 5 = -1/2\color(red)((-4)) - 5 = 2-5 = -3$

How do you find the solution of the system of equations x-2y=2x-2y=2 and y= -1/2x-5y= -1/2x-5?