Question

Solve for $xandy$

$9+25xy=53x;27-4xy=x$

Answer 1

Step 1 :Solving for x and y using elimination method

Given,

$$\begin{gathered} 9+25xy=53x......................................\left(1\right) \\ 27-4xy=x............................................\left(2\right) \end{gathered}$$

Making the coefficients of as same for that

$$\begin{gathered} Equation\left(1\right)\times 4\Rightarrow 36+100xy=212x.................................\left(3\right) \\ \left(2\right)\times 25\Rightarrow 675-100xy=25x...........................................\left(4\right) \\ \left(3\right)+\left(4\right)\Rightarrow 711=237x \\ \Rightarrow x=\frac{711}{237}=3 \end{gathered}$$

Step 2 : Finding ‘y’ by substitution method

Substitute $x=3$ in equation (2)

$$\begin{gathered} \left(2\right)\Rightarrow 27-4\times 3\times y=3 \\ \Rightarrow 27-12y=3 \\ \Rightarrow 27-3=12y \\ \Rightarrow 24=12y \\ \Rightarrow y=\frac{24}{12}=2 \end{gathered}$$

Therefore the values of $x=3andy=2$