Question

Use the substitution method.

2x+4y=16
x-7=-4y


A. (0,-7)
B.(0,7/4)
C.(9,-1/2)
D.(17,-5/2)

Answer 1

Here we have..

`\begin{bmatrix}2x+4y=16\\ x-7=-4y\end{bmatrix}`


`Isolate\;x\;for\;2x+4y=16`


`\mathrm{Subtract\:}4y\mathrm{\:from\:both\:sides} \ \textgreater \ 2x+4y-4y=16-4y`


`Simplify \ \textgreater \ 2x=16-4y \ \textgreater \ \mathrm{Divide\:both\:sides\:by\:}2 \ \textgreater \ (2x)/(2)=(16)/(2)-(4y)/(2)`


`Simplify\;further\;(2x)/(2) \ \textgreater \ \mathrm{Divide\:the\:numbers:}\:(2)/(2)=1 \ \textgreater \ x`


`(16)/(2)-(4y)/(2) \ \textgreater \ \mathrm{Apply\:rule}\:(a)/(c)\pm (b)/(c)=(a\pm \:b)/(c) \ \textgreater \ (16-4y)/(2)`


`16-4y \ \textgreater \ Rewrite \ \textgreater \ 4\cdot \:4-4y \ \textgreater \ \mathrm{Factor\:out\:common\:term\:}4`

`4\left(-y+4\right)`


`(4\left(-y+4\right))/(2) \ \textgreater \ \mathrm{Divide\:the\:numbers:}\:(4)/(2)=2 \ \textgreater \ x = 2\left(-y+4\right)`


`\mathrm{Subsititute\:}x=2\left(-y+4\right) \ \textgreater \ \begin{bmatrix}2\left(-y+4\right)-7=-4y\end{bmatrix}`


`Isolate\;y\;for\;2\left(-y+4\right)-7=-4y`


`Expand\2\left(-y+4\right)-7`

`\mathrm{Distribute\:parentheses\:using}: \:a\left(b+c\right)=ab+ac`

`Where\;a=2,\:b=-y,\:c=4`


`2\left(-y\right)+2\cdot \:4 \ \textgreater \ \mathrm{Apply\:minus-plus\:rules} \ \textgreater \ +\left(-a\right)=-a \ \textgreater \ -2y+2\cdot \:4`


`\mathrm{Multiply\:the\:numbers:}\:2\cdot \:4=8 \ \textgreater \ -2y+8 \ \textgreater \ -2y+8-7`


`\mathrm{Add/Subtract\:the\:numbers:}\:8-7=1 \ \textgreater \ -2y+1 \ \textgreater \ -2y+1=-4y`


`\mathrm{Subtract\:}1\mathrm{\:from\:both\:sides} \ \textgreater \ -2y+1-1=-4y-1 \ \textgreater \ Simplify`

`-2y=-4y-1`


`\mathrm{Add\:}4y\mathrm{\:to\:both\:sides} \ \textgreater \ -2y+4y=-4y-1+4y \ \textgreater \ Simplify`

`2y=-1`


`\mathrm{Divide\:both\:sides\:by\:}2 \ \textgreater \ (2y)/(2)=(-1)/(2) \ \textgreater \ Simplify \ \textgreater \ y=-(1)/(2)`


`\mathrm{For\:}x=2\left(-y+4\right), \mathrm{Subsititute\:}y=-(1)/(2) \ \textgreater \ x=2\left(-\left(-(1)/(2)\right)+4\right) \Rightarrow x=9`


`Therefore\;our\;solutions\;are\;y=-(1)/(2),\:x=9`

Hope this helps!