Question

by elimination method​

Answer 1

Step-by-step explanation:

$11x + 15y + 23 = 0..........(i) \times 7 \\ 7x - 2y - 20..........(ii) \times 11 \\ equation(i) \times 7 - (ii) \times 11 \\ 77 x + 105 y + 161 \\ 77x - 22y - 220 \\ - \: \: \: \: \: + \: \: \: \: \: \: \: + \\ \frac{}{ \: \: \: \: \: \: 127y + 381 = 0} \\ 127y = - 381 \\ y =-3 \\ value \: of \: y \: put \: in \: any \: equation \: then \: the \: value \: of \: x \: will \: come.$

Answer 2

Answer:

$11x+15y+23=0,\:7x-2y-20=0\quad :\quad y=-3,\:x=2$

Step-by-step explanation:

$\begin{bmatrix}11x+15y+23=0\\ 7x-2y-20=0\end{bmatrix}$

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

$\begin{bmatrix}11x+15y=-23\\ 7x-2y=20\end{bmatrix}$

$\mathrm{Multiply\:}11x+15y=-23\mathrm{\:by\:}7:\quad 77x+105y=-161$

$\mathrm{Multiply\:}7x-2y=20\mathrm{\:by\:}11:\quad 77x-22y=220$

$\begin{bmatrix}77x+105y=-161\\ 77x-22y=220\end{bmatrix}$

$77x-22y=220$

$-$

$\underline{77x+105y=-161}$

$-127y=381$

$\begin{bmatrix}77x+105y=-161\\ -127y=381\end{bmatrix}$

$\mathrm{Solve}\:-127y=381\:\mathrm{for}\:y$

$-127y=381$

$\mathrm{Divide\:both\:sides\:by\:}-127$

$\frac{-127y}{-127}=\frac{381}{-127}$

$\mathrm{Simplify}$

$y=-3$

$\mathrm{For\:}77x+105y=-161\mathrm{\:plug\:in\:}\quad \:y=-3$

$\mathrm{Solve}\:77x+105\left(-3\right)=-161\:\mathrm{for}\:x$

$77x+105\left(-3\right)=-161$

$\mathrm{Remove\:parentheses}:\quad \left(-a\right)=-a$

$77x-105\cdot \:3=-161$

$\mathrm{Multiply\:the\:numbers:}\:105\cdot \:3=315$

$77x-315=-161$

$\mathrm{Add\:}315\mathrm{\:to\:both\:sides}$

$77x-315+315=-161+315$

$\mathrm{Simplify}$

$77x=154$

$\mathrm{Divide\:both\:sides\:by\:}77$

$\frac{77x}{77}=\frac{154}{77}$

$\mathrm{Simplify}$

$x=2$

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

$y=-3,\:x=2$