Here we have..
[tex]\begin{bmatrix}2x+4y=16\\ x-7=-4y\end{bmatrix}[/tex]
[tex]Isolate\;x\;for\;2x+4y=16[/tex]
[tex]\mathrm{Subtract\:}4y\mathrm{\:from\:both\:sides} \ \textgreater \ 2x+4y-4y=16-4y[/tex]
[tex]Simplify \ \textgreater \ 2x=16-4y \ \textgreater \ \mathrm{Divide\:both\:sides\:by\:}2 \ \textgreater \ \frac{2x}{2}=\frac{16}{2}-\frac{4y}{2}[/tex]
[tex]Simplify\;further\;\frac{2x}{2} \ \textgreater \ \mathrm{Divide\:the\:numbers:}\:\frac{2}{2}=1 \ \textgreater \ x[/tex]
[tex]\frac{16}{2}-\frac{4y}{2} \ \textgreater \ \mathrm{Apply\:rule}\:\frac{a}{c}\pm \frac{b}{c}=\frac{a\pm \:b}{c} \ \textgreater \ \frac{16-4y}{2}[/tex]
[tex]16-4y \ \textgreater \ Rewrite \ \textgreater \ 4\cdot \:4-4y \ \textgreater \ \mathrm{Factor\:out\:common\:term\:}4 [/tex]
[tex]4\left(-y+4\right)[/tex]
[tex]\frac{4\left(-y+4\right)}{2} \ \textgreater \ \mathrm{Divide\:the\:numbers:}\:\frac{4}{2}=2 \ \textgreater \ x = 2\left(-y+4\right) [/tex]
[tex]\mathrm{Subsititute\:}x=2\left(-y+4\right) \ \textgreater \ \begin{bmatrix}2\left(-y+4\right)-7=-4y\end{bmatrix}[/tex]
[tex]Isolate\;y\;for\;2\left(-y+4\right)-7=-4y [/tex]
[tex]Expand\2\left(-y+4\right)-7[/tex]
[tex]\mathrm{Distribute\:parentheses\:using}: \:a\left(b+c\right)=ab+ac[/tex]
[tex]Where\;a=2,\:b=-y,\:c=4[/tex]
[tex]2\left(-y\right)+2\cdot \:4 \ \textgreater \ \mathrm{Apply\:minus-plus\:rules} \ \textgreater \ +\left(-a\right)=-a \ \textgreater \ -2y+2\cdot \:4[/tex]
[tex]\mathrm{Multiply\:the\:numbers:}\:2\cdot \:4=8 \ \textgreater \ -2y+8 \ \textgreater \ -2y+8-7[/tex]
[tex]\mathrm{Add/Subtract\:the\:numbers:}\:8-7=1 \ \textgreater \ -2y+1 \ \textgreater \ -2y+1=-4y[/tex]
[tex]\mathrm{Subtract\:}1\mathrm{\:from\:both\:sides} \ \textgreater \ -2y+1-1=-4y-1 \ \textgreater \ Simplify[/tex]
[tex]-2y=-4y-1[/tex]
[tex]\mathrm{Add\:}4y\mathrm{\:to\:both\:sides} \ \textgreater \ -2y+4y=-4y-1+4y \ \textgreater \ Simplify[/tex]
[tex]2y=-1[/tex]
[tex]\mathrm{Divide\:both\:sides\:by\:}2 \ \textgreater \ \frac{2y}{2}=\frac{-1}{2} \ \textgreater \ Simplify \ \textgreater \ y=-\frac{1}{2}[/tex]
[tex]\mathrm{For\:}x=2\left(-y+4\right), \mathrm{Subsititute\:}y=-\frac{1}{2} \ \textgreater \ x=2\left(-\left(-\frac{1}{2}\right)+4\right) \Rightarrow x=9[/tex]
[tex]Therefore\;our\;solutions\;are\;y=-\frac{1}{2},\:x=9[/tex]
Hope this helps!
