How do you solve $15x-10y=-5$ and $15y=5+10x$ using substitution?

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Answer 1 · 2018-06-27T01:15:40

$x=-1/5, y=1/5$

Since every term in both equations is divisible by $5$ , let's divide every term by this. We now have the equations

$3x-2y=-1$

$3y=1+2x$

In the second equation, let's divide all terms by $3$ to solve for $y$ . We get

$color(blue)(y=2/3x+1/3)$

This is where the substitution comes in...let's plug this value for $y$ into the first equation.

$3x-2color(blue)((2/3x+1/3))=-1$

Distributing the $-2$ , we get

$3x-4/3x-2/3=-1$

Let's make all terms have a common denominator:

$9/3x-4/3x-2/3=-3/3$

Now, we can simplify this further:

$5/3x-2/3=-3/3$

$=>5/3x=-1/3$

$=>5x=-1$

$=>color(darkviolet)(x=-1/5)$

Let's solve for $y$ now. We can plug this $x$ value into our blue equation:

$y=2/3color(darkviolet)((-1/5))+1/3$

$=>y=-2/15+1/3$

$=>y=-2/15+5/15=3/15=1/5$

$x=-1/5, y=1/5$

Hope this helps!

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