Question

solve for x and y : 3/2(x+2y)=5 , 3/5(2x-y)=2​

Answer 1

Answer:

y=2/3

and x=2

Step-by-step explanation:

hope it helps you

Answer 2

Answer

$\sf \dashrightarrow \dfrac{3}{2} (x + 2y) = 5 \: \: --- (i)$

$\sf \dashrightarrow \dfrac{3}{5}(2x - y) = 2 \: \: --- (ii)$

By first equation,

$\sf \dashrightarrow \dfrac{3}{2} (x + 2y) = 5$

$\sf \dashrightarrow \dfrac{3x}{2} + \dfrac{6y}{2} = 5$

$\sf \dashrightarrow \dfrac{3x + 6y}{2} = 5$

$\sf \dashrightarrow 3x + 6y = 5 \times 2$

$\sf \dashrightarrow 3x + 6y = 10 \: \: --- (iii)$

By second equation,

$\sf \dashrightarrow \dfrac{3}{5} (2x - y) = 2$

$\sf \dashrightarrow \dfrac{6x}{5} - \dfrac{3y}{5} = 2$

$\sf \dashrightarrow \dfrac{6x - 3y}{5} = 2$

$\sf \dashrightarrow 6x - 3y = 5 \times 2$

$\sf \dashrightarrow 6x - 3y = 10 \: \: --- (iv)$

Now, by third equation,

$\sf \dashrightarrow 3x + 6y = 10$

$\sf \dashrightarrow 3x = 10 - 6y$

$\sf \dashrightarrow x = \dfrac{10 - 6y}{3}$

Now, let's find the value of y by fourth equation.

$\sf \dashrightarrow 6x - 3y = 10$

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

$\sf \dashrightarrow \dfrac{60 - 36y}{3} - 3y = 10$

$\sf \dashrightarrow \dfrac{60 - 36y - 9y}{3} = 10$

$\sf \dashrightarrow \dfrac{60 - 45y}{3} = 10$

$\sf \dashrightarrow 60 - 45y = 10 \times 3$

$\sf \dashrightarrow 60 - 45y = 30$

$\sf \dashrightarrow -45y = 30 - 60$

$\sf \dashrightarrow -45y = -30$

$\sf \dashrightarrow y = \dfrac{-30}{-45}$

$\sf \dashrightarrow y = \dfrac{2}{3}$

Now, let's find the value of y by fourth equation.

$\sf \dashrightarrow 6x - 3y = 10$

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

$\sf \dashrightarrow 6x - \dfrac{6}{3} = 10$

$\sf \dashrightarrow 6x - 2 = 10$

$\sf \dashrightarrow 6x = 10 + 2$

$\sf \dashrightarrow 6x = 12$

$\sf \dashrightarrow x = \dfrac{12}{6}$

$\sf \dashrightarrow x = 2$

Hence, the values of x and y are 2 and 2/3 respectively.