Question

Solve the following systems of simultaneous linear equation by the elimination method
x/6 = y-6
3x= 1+y


pls solve step by step​

Answer 1

Answer:

$\dfrac{x}{6}=y-6,\:3x=1+y\quad :\quad y=\dfrac{109}{17},\:x=\dfrac{42}{17}$

Step-by-step explanation:

$\begin{bmatrix}\dfrac{x}{6}=y-6\\ 3x=1+y\end{bmatrix}$

$\mathrm{Arrange\:equation\:variables\:for\:elimination}$

$\begin{bmatrix}\dfrac{1}{6}x-y=-6\\ 3x-y=1\end{bmatrix}$

$\mathrm{Multiply\:}\dfrac{1}{6}x-y=-6\mathrm{\:by\:}18:\quad 3x-18y=-108$

$\begin{bmatrix}3x-18y=-108\\ 3x-y=1\end{bmatrix}$

  $3x-y=1$

$-$

  $\underline{3x-18y=-108}$

  $17y=109$

$\begin{bmatrix}3x-18y=-108\\ 17y=109\end{bmatrix}$

$\mathrm{Solve}\:17y=109\:\mathrm{for}\:y$

$17y=109$

$\mathrm{Divide\:both\:sides\:by\:}17$

$\dfrac{17y}{17}=\dfrac{109}{17}$

$\mathrm{Simplify}$

$y=\dfrac{109}{17}$

$\mathrm{For\:}3x-18y=-108\mathrm{\:plug\:in\:}\quad \:y=\dfrac{109}{17}$

$\mathrm{Solve}\:3x-18\cdot\dfrac{109}{17}=-108\:\mathrm{for}\:x$

$3x-18\cdot \dfrac{109}{17}=-108$

$\mathrm{Add\:}18\cdot\dfrac{109}{17}\mathrm{\:to\:both\:sides}$

$3x-18\cdot \dfrac{109}{17}+18\cdot \dfrac{109}{17}=-108+18\cdot \dfrac{109}{17}$

$\mathrm{Simplify}$

$3x=\dfrac{126}{17}$

$\mathrm{Divide\:both\:sides\:by\:}3$

$\dfrac{3x}{3}=\dfrac{\dfrac{126}{17}}{3}$

$\mathrm{Simplify}$

$x=\dfrac{42}{17}$

$\mathrm{The\:solutions\:to\:the\:system\:of\:equations\:are:}$

$y=\dfrac{109}{17},\:x=\dfrac{42}{17}$

Answer 2

$\dfrac{x}{6}$ = y - 6

3x = 1 + y

_________ [GIVEN EQUATIONS]

____________________________

» Refer the Attachment.

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x = $\dfrac{42}{17}$

y = $\dfrac{109}{17}$

____________ [ANSWER]