Question

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

Answer 1

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;

$$\begin{gathered} \begin{array}{rcl}& & 6\end{array}\begin{array}{rcl}& & x\end{array}\begin{array}{rcl}& & +\end{array}\begin{array}{rcl}& & 8\end{array}\begin{array}{rcl}& & y\end{array}\begin{array}{rcl}& & -\end{array}\begin{array}{rcl}& & 6\end{array}\begin{array}{rcl}& & x\end{array}\begin{array}{rcl}& & -\end{array}\begin{array}{rcl}& & 7\end{array}\begin{array}{rcl}& & y\end{array}\begin{array}{rcl}& =& \end{array}\begin{array}{rcl}& & 170\end{array}\begin{array}{rcl}& & -\end{array}\begin{array}{rcl}& & 20\end{array} \\ \begin{array}{rcl}& \Rightarrow & y=150\end{array} \end{gathered}$$

Putting value $y$ of in equation (i)

$\begin{array}{rcl}3x+4\left(150\right)& =& 85\\ & \Rightarrow & 3x=85-600\\ & \Rightarrow & 3x=-515\\ & \Rightarrow & x=-\frac{515}{3}\end{array}$

Hence, the value $x$ is $-\frac{515}{3}$ and $y$ is $150$.