Question

Solve the following sets of simultaneous equations.
$2y-x=0;10x+15y=105$

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

Answer 1

Answer: (A)

$x=6,y=3$

To solve $2y-x=0$

$10x+15y=105$

$2y-x=0\iff –x+2y=0$

$-[x-2y]=0\Rightarrow x-2y=0$ equation $1$

$10x=15y=105\iff 5[2x+3y]$

$\Rightarrow$\quad 2x-3y=2\rightarrow$equation$2$

From eq $1$ we get, $x-2y=0$

$\Rightarrow x=2y$

Let us substitute ${}^{\prime }{x}^{\prime }$ in eq $2$ we get,

$2\left[2y\right]+3y=21\iff 4y+3y=21$

$\Rightarrow 7y=21\iff 21/7=3\therefore y=3$

Let us now substitute${}^{\prime }{y}^{\prime }$ Value in $x=2y$

We get,$x=2\left(3\right)\Rightarrow x=6$

$\therefore$ after solving equations $2y-x0$&$10x+15y=105$ we get,

$x=6,y=3$

Correct option is $\left[a\right]$