How do you solve using elimination of $5 x + 4 y + 2 = 0$ $5x+4y+2=0$ and $4 x - 5 y - 23 = 0$ $4x-5y-23=0$ ?

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Answer 1 · 2018-03-08T14:21:58

$x = 2$ $x=2$
$y = - 3$ $y=-3$

$5 x + 4 y + 2 = 0$ $5x+4y+2=0$

$\Rightarrow 5 x + 4 y = - 2$ $=> 5x+4y=-2$

Multiply 5 both sides

$\Rightarrow 25 x + 20 y = - 10$ $=> 25x+20y=-10$ ----(1)

$4 x - 5 y - 23 = 0$ $4x-5y-23=0$

$\Rightarrow 4 x - 5 y = 23$ $=>4x-5y=23$ ----(2)

Multiply 4 both sides

$\Rightarrow 16 x - 20 y = 92$ $=>16x-20y=92$ ----(3)

$(1) + (3)$ $(1) + (3)$

$\Rightarrow 25 x + 20 y + 16 x - 20 y = - 10 + 92$ $=> 25x+20y+16x-20y=-10+92$

$\Rightarrow 41 x = 82$ $=> 41x=82$

$\Rightarrow x = 2$ $=> x=2$

Put this value in $(2)$ $(2)$

$\Rightarrow 4 (2) - 5 y = 23$ $=> 4(2)-5y=23$

$\Rightarrow 8 - 5 y = 23$ $=> 8-5y=23$

$\Rightarrow 8 - 23 = 5 y$ $=> 8-23=5y$

$\Rightarrow - 15 = 5 y$ $=> -15=5y$

$\Rightarrow - 3 = y$ $=> -3=y$

How do you solve using elimination of 5x+4y+2=0 5x+4y+2=05x+4y+2=0 and 4x-5y-23=04x−5y−23=04x-5y-23=0?