Math, asked by neelimagoel23, 1 year ago

Solve by Eliminating
43x – 37y = 31; 13x + 23y = – 59

Answers

Answered by vedansh074
2

Answer:

please refer to attachment

Attachments:
Answered by AbhijithPrakash
9

Answer:

43x-37y=31,\:13x+23y=-59\quad :\quad y=-2,\:x=-1

Step-by-step explanation:

\begin{bmatrix}43x-37y=31\\ 13x+23y=-59\end{bmatrix}

\gray{\mathrm{Multiply\:}43x-37y=31\mathrm{\:by\:}13:\quad 559x-481y=403}

\gray{\mathrm{Multiply\:}13x+23y=-59\mathrm{\:by\:}43:\quad 559x+989y=-2537}

\begin{bmatrix}559x-481y=403\\ 559x+989y=-2537\end{bmatrix}

  \gray{559x+989y=-2537}

\gray{-}

  \gray{\underline{559x-481y=403}}

  \gray{1470y=-2940}

\begin{bmatrix}559x-481y=403\\ 1470y=-2940\end{bmatrix}

\black{\mathrm{Solve}\:1470y=-2940\:\mathrm{for}\:y:}

1470y=-2940

\gray{\mathrm{Divide\:both\:sides\:by\:}1470}

\dfrac{1470y}{1470}=\dfrac{-2940}{1470}

\gray{\mathrm{Simplify}}

y=-2

\gray{\mathrm{For\:}559x-481y=403\mathrm{\:plug\:in\:}\quad \:y=-2}

559x-481\left(-2\right)=403

\gray{\mathrm{Apply\:rule}\:-\left(-a\right)=a}

559x+481\cdot \:2=403

\gray{\mathrm{Multiply\:the\:numbers:}\:481\cdot \:2=962}

559x+962=403

\gray{\mathrm{Subtract\:}962\mathrm{\:from\:both\:sides}}

559x+962-962=403-962

\gray{\mathrm{Simplify}}

559x=-559

\gray{\mathrm{Divide\:both\:sides\:by\:}559}

\dfrac{559x}{559}=\dfrac{-559}{559}

\gray{\mathrm{Simplify}}

x=-1

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

y=-2,\:x=-1

\black{\mathrm{Solve}\:559x-481\left(-2\right)=403\:\mathrm{for}\:x:}

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