How do you solve 15x - 20y = 1 and 5y = 1 + 10x using substitution?

Mar 20, 2016

$x , y = - \frac{1}{5}$

Explanation:

color(blue)(15x-20y=1

color(blue)(5y=1+10x

Use the second equation

$\rightarrow 5 y = 1 + 10 x$

Divide both sides by $5$

$\rightarrow \frac{\cancel{5} y}{\cancel{5}} = \frac{1 + 10 x}{5}$

$\rightarrow y = \frac{1}{5} + 2 x$

Now substitute this value to the first equation

$\rightarrow 15 x - 20 \left(\frac{1}{5} + 2 x\right) = 1$

Use the distributive property color(brown)(a(b+c)=ab+ac

$\rightarrow 15 x - \frac{20}{5} - 40 x = 1$

$\rightarrow 15 x - 4 - 40 x = 1$

$\rightarrow - 25 x - 4 = 1$

Add $4$ both sides

$\rightarrow - 25 x \cancel{- 4 + 4} = 1 + 4$

$\rightarrow - 25 x = 5$

color(green)(rArrx=-5/25=-1/5

Substitute the value of $x$ to the second equation

$\rightarrow 5 y = 1 + 10 \left(- \frac{1}{5}\right)$

$\rightarrow 5 y = 1 - \frac{10}{5}$

$\rightarrow 5 y = 1 - 2$

$\rightarrow 5 y = - 1$

color(green)(y=-1/5

:. color(indigo)(ul bar |x=y=-1/5|