Question

solve the elimination method
2x+3y=5
5x+2y=3​

Answer 1

The required solution of $2x+3y=5$ and $5x+2y=3$ is $x=-\dfrac{1}{11},y=\dfrac{19}{11}$.

Step-by-step explanation:

Here, the given equations are

$2x+3y=5\to (i)\\ 5x+2y=3\to (ii)$

Multiplying (i) no. equation by $5$ and (ii) no. equation by $2$, we get

$10x+15y=25\\ 10x+4y=6$

On subtraction, we get

$\quad 11y=19$

$\Rightarrow \boxed{y=\dfrac{19}{11}}$

Putting $y=\dfrac{19}{11}$ in (i) no. equation, we get

$\quad 2x+\dfrac{57}{11}=5$

$\Rightarrow 2x=5-\dfrac{57}{11}$ [We have transposed $\dfrac{57}{11}$ to the right hand side.]

$\Rightarrow 2x=\dfrac{55-57}{11}$

$\Rightarrow 2x=-\dfrac{2}{11}$

$\Rightarrow \boxed{x=-\dfrac{1}{11}}$

Therefore the required solution is

$\quad x=-\dfrac{1}{11},y=\dfrac{19}{11}$