Question

solve linear equations "-x-y=5;-x+4y=15"

Who says correct and fast I will mark as brainalist...
it's for sure...​

Answer 1

★ Solution :-

$\sf \leadsto - x - y = 5 \: \: - - - (i)$

$\sf \leadsto - x + 4y = 15 \: \: - - - (ii)$

Now, by multiplying the whole first equation by 4,

$\sf \leadsto 4(- x - y = 5)$

$\sf \leadsto - 4x - 4y = 20$

Now, by adding both equations,

$\sf \: \: \: \: - 4x - 4y = 20 \\ \sf + \: \: \: \: \: \: (-x + 4y = 15)$

$\sf \: \: - 4x - 4y = 20 \\ \sf + \: \: \: \: - x + 4y = 15$

$\sf \leadsto -5x -0 = 35$

$\sf \leadsto - 5x = 35$

$\sf \leadsto x = \dfrac{35}{-5}$

$\sf \leadsto x = -7$

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

$\sf \leadsto - x - y = 5$

$\sf \leadsto -(-7) - y = 5$

$\sf \leadsto 7 - y = 5$

$\sf \leadsto -y = 5 - 7$

$\sf \leadsto -y = -2$

$\sf \leadsto y = 2$

Therefore, the values of x and y are -7 and 2 respectively.

Answer 2

Solution :-

$\sf\leadsto \: - x - y = 5 \: ( \: equation \: 1) \: \: \: \: \\ \sf\leadsto \: - x + 4y = 15 \: ( \: equation \: 2)$

Now, we will multiply equation (i) by 4 , we get,

$\sf\leadsto \: 4( - x - y )= 4 \times 5 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \sf \leadsto \: - 4x - 4y = 20 \: ( \: equation \: 3)$

Now, we will add equation (iii) and equation (ii),

$\sf \leadsto \:( - 4x - 4y) + ( - x + 4y) = 20 + 15 \\ \sf \leadsto \: - 4x - x \: \cancel{- 4y } \: \cancel {+ 4y} = 35 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \sf \leadsto \: - 5x = 35 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \sf \leadsto \: x = \frac{35}{ - 5} = - 7 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:$

Now, putting the value of x in equation (i), we get,

$\sf \leadsto \: - x - y = 5 \: \: \: \: \: \: \: \\ \sf \leadsto \: - ( - 7) - y = 5 \\ \sf \leadsto \: + 7 - y = 5 \: \: \: \: \: \: \: \\ \sf \leadsto - y = - 2 \: \: \: \: \: \: \: \: \: \: \: \: \\ \sf \leadsto \: y = 2 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:$

$\sf \therefore \red {x = - 7} \\ \sf \orange {and \: y = 2}$