Question

# $3x+4y=85$ and $6x+7y=20$. Find $x$ and $y$.

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Solution

## Step 1: Changing one equation by multiplying it with a constant.Given :$3x+4y=85$ . . .(i)$6x+7y=20$ . . .(ii)Multiplying equation (i) with $2$.$6x+8y=170$ . . .(iii)Step 2: Finding the value of $x$ and $y$.Subtracting (ii) from (iii), we get;$\begin{array}{rcl}& & 6\end{array}\begin{array}{rcl}& & x\end{array}\begin{array}{rcl}& & +\end{array}\begin{array}{rcl}& & 8\end{array}\begin{array}{rcl}& & y\end{array}\begin{array}{rcl}& & -\end{array}\begin{array}{rcl}& & 6\end{array}\begin{array}{rcl}& & x\end{array}\begin{array}{rcl}& & -\end{array}\begin{array}{rcl}& & 7\end{array}\begin{array}{rcl}& & y\end{array}\begin{array}{rcl}& =& \end{array}\begin{array}{rcl}& & 170\end{array}\begin{array}{rcl}& & -\end{array}\begin{array}{rcl}& & 20\end{array}\phantom{\rule{0ex}{0ex}}\begin{array}{rcl}& ⇒& y=150\end{array}$Putting value $y$ of in equation (i)$\begin{array}{rcl}3x+4\left(150\right)& =& 85\\ & ⇒& 3x=85-600\\ & ⇒& 3x=-515\\ & ⇒& x=-\frac{515}{3}\end{array}$Hence, the value $x$ is $-\frac{515}{3}$ and $y$ is $150$.

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