Question

hi guys pls help me with this question. 4x-5y=6;5x+5y=6​

Answer 1

Answer

$\sf \dashrightarrow 4x - 5y = 6 \: \: --- (i)$

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

By first equation,

$\sf \dashrightarrow 4x - 5y = 6$

$\sf \dashrightarrow 4x = 6 + 5y$

$\sf \dashrightarrow x = \dfrac{6 + 5y}{4}$

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

$\sf \dashrightarrow 5x + 5y = 6$

$\sf \dashrightarrow 5 \bigg( \dfrac{6 + 5y}{4} \bigg) + 5y = 6$

$\sf \dashrightarrow \dfrac{30 + 25y}{4} + 5y = 6$

$\sf \dashrightarrow \dfrac{30 + 25y + 20y}{4} = 6$

$\sf \dashrightarrow \dfrac{30 + 45y}{4} = 6$

$\sf \dashrightarrow 30 + 45y = 4 \times 6$

$\sf \dashrightarrow 30 + 45y = 24$

$\sf \dashrightarrow 45y = 25 - 30$

$\sf \dashrightarrow 45y = -5$

$\sf \dashrightarrow y = \dfrac{-5}{45}$

$\sf \dashrightarrow y = \dfrac{-1}{9}$

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

$\sf \dashrightarrow 4x - 5y = 6$

$\sf \dashrightarrow 4x - 5 \bigg( \dfrac{-1}{9} \bigg) = 6$

$\sf \dashrightarrow 4x - \dfrac{-5}{9} = 6$

$\sf \dashrightarrow 4x = 6 + \dfrac{-5}{9}$

$\sf \dashrightarrow 4x = \dfrac{54 + (-5)}{9}$

$\sf \dashrightarrow 4x = \dfrac{49}{9}$

$\sf \dashrightarrow x = \dfrac{49}{9} \times \dfrac{1}{4}$

$\sf \dashrightarrow x = \dfrac{49}{36}$

Hence, the values of x and y are $\sf \dfrac{49}{36}$ and $\sf \dfrac{-1}{9}$ respectively.