Question

-2x+3y=10;2x-5y=6 solve

Answer 1

Answer:

−

2

+

3

=

1

0

;

2

−

5

=

6

Step-by-step explanation:

Answer 2

Answer

$\sf \dashrightarrow -2x + 3y = 10 \: \: --- (i)$

$\sf \dashrightarrow 2x - 5y = 6 \: \: --- (ii)$

Finding x by equation i,

$\sf \dashrightarrow -2x + 3y = 10$

$\sf \dashrightarrow -2x = 10 - 3y$

$\sf \dashrightarrow x = \dfrac{10 - 3y}{-2}$

Now, we can find the value of y by the second equation,

$\sf \dashrightarrow 2x - 5y = 6$

$\sf \dashrightarrow 2 \bigg( \dfrac{10 - 3y}{-2} \bigg) - 5y = 6$

$\sf \dashrightarrow \dfrac{20 - 6y}{2} - 5y = 6$

$\sf \dashrightarrow \dfrac{20 - 6y - 10y}{2} = 6$

$\sf \dashrightarrow \dfrac{20 - 16y}{2} = 6$

$\sf \dashrightarrow 20 - 16y = 6 \times 2$

$\sf \dashrightarrow 20 - 16y = 12$

$\sf \dashrightarrow -16y = 12 - 20$

$\sf \dashrightarrow -16y = -8$

$\sf \dashrightarrow y = \dfrac{-8}{-16}$

$\sf \dashrightarrow y = \dfrac{1}{2}$

Now, we can find the value of x by first equation.

$\sf \dashrightarrow -2x + 3y = 10$

$\sf \dashrightarrow -2x + 3 \bigg( \dfrac{1}{2} \bigg) = 10$

$\sf \dashrightarrow -2x + \dfrac{3}{2} = 10$

$\sf \dashrightarrow -2x = 10 - \dfrac{3}{2}$

$\sf \dashrightarrow -2x = \dfrac{20 - 3}{2}$

$\sf \dashrightarrow -2x = \dfrac{17}{2}$

$\sf \dashrightarrow x = \dfrac{\dfrac{17}{2}}{-2}$

$\sf \dashrightarrow x = \dfrac{17}{2} \times \dfrac{-1}{2}$

$\sf \dashrightarrow x = \dfrac{-17}{4}$

Hence, the values of x and y are $\sf \dfrac{-17}{4}$ and $\sf \dfrac{1}{2}$ respectively.