Question #44498

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Answer 1 · 2017-09-21T18:01:36

$x = 12 and y = 8$ $color(green)(x=12 and y=8)$

Let the two numbers be x and y.

So from what you said we know that $x + y = 20$ $x+y = 20$ .

We also know that $x - y = 4$ $x-y = 4$ .

Now if we rearrange the equation to make x the subject we get.

$x = y + 4$ $x=y+4$

Now that we know the value of x let's substitute this into the equation $x + y = 20$ $x+y=20$ .

$(y + 4) + y = 20$ $(y+4)+y = 20$ this can be rewritten as $2 y + 4 = 20$ $2y+4 = 20$

Let's solve it!

Subtract both sides by 4

$2 y + 4 (- 4) = 20 (- 4)$ $2y+4 color(red)((-4))=20color(red)((-4)$

this gives us

$2 y = 16$ $2y=color(green)(16)$

Divide both sides by 2

$2 y \div 2 = 16 \div 2$ $2y color(red)(÷2)= 16color(red)(÷2)$

this gives us

$y = 8$ $color(green)(y = 8)$

Now let us find the value of x via substitution.

$x + 8 = 20$ $x+8=20$

Subtract both sides by 8
$x + 8 (- 8) = 20 (- 8)$ $x+8color(red)((-8))=20color(red)((-8)$

so we get x as

$x = 12$ $color(green)(x=12)$