Question

Solve the following simultaneous equations:

$15x-17y=28;15y-17x+36=0$

• A. $x=3$, $y=1$
• B. $x=-3$, $y=1$
• C. $x=6$, $y=2$
• D. $x=2$, $y=3$

Answer 1

The correct option is A $x=3$, $y=1$

Consider the equations:

$15x-17y=\mathrm{28........}\left(1\right)$ and

$-17x+15y=-\mathrm{36........}\left(2\right)$

Multiplying equation 1 by $17$ and equation 2 by $15$, we get:

$255x-289y=\mathrm{476........}\left(3\right)$ and

$-255x+225y=-\mathrm{540........}\left(4\right)$

Now adding equations 3 and 4 we get:

$255x-289y-255x+225y=476-540$

or $64y=64$

or $y=1$

Substitute the value of $y$ in equation 1:

$15x-17=28$

$15x=45$

$x=3$

Hence, $x=3,y=1$.