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

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Answer 1 · 2018-06-15T07:37:27

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

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

$y = - \frac{1}{2} x - 5$ $y = -1/2x - 5$

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

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

Rearrange this last expression:

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

Subtract $10$ $10$ from both sides:

$2 x = - 8$ $2x = -8$

Divide both sides by $2$ $2$ :

$x = - 4$ $x = -4$

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

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

How do you find the solution of the system of equations x−2y=2x-2y=2 and y=−12x−5y= -1/2x-5?