Question

Solve the system of equations:
$37x+29y=13;29x+37y=53$

Answer 1

Given $37x+29y=13$ ..........(i)
$29x+37y=53$ ............(ii)
Here, we observe that the coefficients of $x$ and $y$ in the first equation are interchanged in the second equation.
Adding these two equations we get:
$37x+29y+29x+37y=53+13$
$\Rightarrow 66x+66y=66$
$\therefore x+y=1$ ................(iii)

Subtracting eq (ii) from (i), we get:
$37x+29y-29x-37y=-53+13$
$\Rightarrow 8x-8y=-40$
$\therefore x-y=-5$..... ...(iv)
Adding (iii) and (iv), we get:
$x+y+x-y=1-5$
$2x-=-4$
$\therefore x=-2$
Substitute the value of $x$ in equation(iii), we get
$-2+y=1$
$y=1+2$
$\therefore y=3$
Hence, $x=-2,y=3$ is the solution of the given system of equations.