Question

What is the simultaneous of the equation :
2x+5y= 14 ,3x-2y=2

Answer 1

Answer

$\sf \dashrightarrow 2x + 5y = 14 \: \: --- (i)$

$\sf \dashrightarrow 3x - 2y = 2 \: \: --- (ii)$

By first equation,

$\sf \dashrightarrow 2x + 5y = 14$

$\sf \dashrightarrow 2x = 14 - 5y$

$\sf \dashrightarrow x = \dfrac{14 - 5y}{2}$

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

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

$\sf \dashrightarrow 3 \bigg( \dfrac{14 - 5y}{2} \bigg) - 2y = 2$

$\sf \dashrightarrow \dfrac{42 - 15y}{2} - 2y = 2$

$\sf \dashrightarrow \dfrac{42 - 15y - 4y}{2} = 2$

$\sf \dashrightarrow \dfrac{42 - 19y}{2} = 2$

$\sf \dashrightarrow 42 - 19y = 2 \times 2$

$\sf \dashrightarrow 42 - 19y = 4$

$\sf \dashrightarrow -19y = 4 - 42$

$\sf \dashrightarrow -19y = -38$

$\sf \dashrightarrow y = \dfrac{-38}{-19}$

$\sf \dashrightarrow y = 2$

Now, let's find the value of x by first equation.

$\sf \dashrightarrow 2x + 5y = 14$

$\sf \dashrightarrow 2x + 5(2) = 14$

$\sf \dashrightarrow 2x + 10 = 14$

$\sf \dashrightarrow 2x = 14 - 10$

$\sf \dashrightarrow 2x = 4$

$\sf \dashrightarrow x = \dfrac{4}{2}$

$\sf \dashrightarrow x = 2$

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