Question

Solve the following simultaneous equations:

$37x+29y=13;29x+37y=53$

• A. $x=1$, $y=4$
• B. $x=3$, $y=-1$
• C. $x=-2$, $y=3$
• D. $x=1$, $y=-2$

Answer 1

Answer: (C)

$x=-2$, $y=3$

Consider the equations:

$37x+29y=\mathrm{13........}\left(1\right)$ and

$29x+37y=\mathrm{53........}\left(2\right)$

Multiplying equation 1 by $29$ and equation 2 by $37$, we get:

$1073x+841y=\mathrm{377........}\left(3\right)$ and

$1073x+1369y=\mathrm{1961........}\left(4\right)$

Now subtracting equations 1 from equation 2 we get:

$1073x+1369y-1073x-841y=1961-377$

or $528y=1584$

or $y=3$

Substitute the value of $y$ in equation 1:

$37x+87=13$

$37x=-74$

$x=-2$

Hence, $x=-2,y=3$.