How do you solve the following system: $1/2x - 2y = 4 , 5x+3y=-1$ ?

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Answer 1 · 2017-05-07T15:25:46

$x = 20/23 and y = -41/23$

The approach is either to use substitution or elimination.

For substitution, you need to have a single variable such as $x$

$1/2x-2y =4" and "5x+3y =-1$

Multiply the first equation by $2$

$2xx1/2x -2xx2y =2xx 4$

$x-4y =8$

$color(blue)(x = (4y+8))" "$ Substitute for $x$ in the other equation:

$color(white)(ml.m)5color(blue)(x)+3y=-1$
$color(white)(mmm)darr$
$color(white)(m)5color(blue)((4y+8)) +3y=-1$

$20y+40 +3y =-1$

$23y = -1-40$

$23y = -41$

$y = (-41)/23$

Now find $x" by using " x = 4y+8$

$x = 4((-41)/23)+8$

$x = 20/23$

Substitute to check:

$5x +3y$

$5(20/23)+3(-41 /23)$

$=100/23-123/23$

$=-1$

How do you solve the following system: 1/2x - 2y = 4 , 5x+3y=-1 1/2x - 2y = 4 , 5x+3y=-1 ?