Question

Solve the following simultaneous equations:
$4x-5y=6;3y-x=2$

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

Answer 1

The correct option is C $x=4,y=2$

Given equations:
$4x-5y=6$ ---- eq. (i)
$3y-x=2$ ---- eq. (ii)

Writing the value of $x$ in terms of $y$ from eq. (ii), we get,
$x=3y-2$ ----eq. (iii)

Now, substituting $x=3y-2$ in eq. (i), we get,
$⟹4(3y-2)-5y=6$
$⟹12y-8-5y=6$
$⟹7y=6+8$
$⟹7y=14$
$⟹y=2$

Now, substituting $y=2$ in eq. (iii), we get,
$⟹x=3\left(2\right)-2$
$⟹x=6-2$
$⟹x=4$

$\therefore x=4$ and $y=2$ is the solution for the given pair of linear equations.