Via subsitution we want to isolate x for 6x - 4y = 36
Start by adding 4y to both sides.
[tex]6x-4y+4y=36+4y \ \textgreater \ Simplify \ \textgreater \ 6x=36+4y[/tex]
Now divide both sides by 6
[tex]\frac{6x}{6}=\frac{36}{6}+\frac{4y}{6}[/tex].
Now simplify further.
[tex] \frac{6x}{6} = \frac{6}{6} = 1 = x[/tex]
Apply the rule of [tex]\frac{a}{c}\pm \frac{b}{c}=\frac{a\pm \:b}{c}[/tex] to [tex]\frac{36}{6}+\frac{4y}{6}[/tex]
When applied > [tex]\frac{36+4y}{6}[/tex] > Now factor 36 + 4y > Rewrite it as....
[tex]4\cdot \:9+4y[/tex] > Factor out the common term of 4 > [tex]4\left(y+9\right)[/tex]
This gives us [tex]\frac{4\left(y+9\right)}{6}[/tex]
From there we want to cancel the common factor of 2 which gives us...
[tex]\frac{2\left(y+9\right)}{3}[/tex]
Now you want to [tex]\mathrm{Subsititute\:}x=\frac{2\left(y+9\right)}{3} \ \textgreater \ \begin{bmatrix}2\cdot \frac{2\left(y+9\right)}{3}-8y=32\end{bmatrix}[/tex]
[tex]2\cdot \frac{2\left(y+9\right)}{3} \ \textgreater \ \mathrm{Multiply\:fractions}:\quad \:a\cdot \frac{b}{c}=\frac{a\:\cdot \:b}{c} \ \textgreater \ \frac{2\left(y+9\right) \cdot \:2}{3}[/tex]
[tex]\mathrm{Multiply\:the\:numbers:}\:2\cdot \:2=4[/tex]
This gives us [tex]\frac{4\left(y+9\right)}{3}[/tex]
So now we have [tex]\frac{4\left(y+9\right)}{3}-8y=32[/tex]
We want to multiply both sides by 3.
[tex]\frac{4\left(y+9\right)}{3}\cdot \:3-8y\cdot \:3=32\cdot \:3[/tex]
Refine it.
[tex]4\left(y+9\right)-24y=96[/tex]
Expand [tex]4\left(y+9\right)[/tex]
[tex]\mathrm{Distribute\:parentheses\:using}:\quad \:a\left(b+c\right)=ab+ac [/tex]
Where [tex]a=4,\:b=y,\:c=9[/tex]
[tex]4\cdot \:y+4\cdot \:9 \ \textgreater \ \mathrm{Multiply\:the\:numbers:}\:4\cdot \:9=36 \ \textgreater \ 4y +36[/tex]
So now we have [tex]4y+36-24y[/tex]
Group the like terms.
[tex]4y-24y+36 \ \textgreater \ \mathrm{Add\:similar\:elements:}\:4y-24y=-20y \ \textgreater \ -20y+36[/tex]
[tex]-20y+36=96 \ \textgreater \ \mathrm{Subtract\:}36\mathrm{\:from\:both\:sides} [/tex]
[tex]-20y+36-36=96-36 \ \textgreater \ Simplify \ \textgreater \ -20y=60 \ \textgreater \ [/tex]
Now we want to [tex]\mathrm{Divide\:both\:sides\:by\:}-20 \ \textgreater \ \frac{-20y}{-20}=\frac{60}{-20} \ \textgreater \ y=-3[/tex]
[tex]\mathrm{For\:}x=\frac{2\left(y+9\right)}{3} \ \textgreater \ \mathrm{Subsititute\:}y=-3 \ \textgreater \ x=\frac{2\left(-3+9\right)}{3}\quad \Rightarrow \quad x=4[/tex]
Therefore our final solutions are, y = -3, x =4.
Hope this helps!
