X+4y=27/X+2y=21

Solution for X+4y=27/X+2y=21 equation:

X+4X=27/X+2X=21

We move all terms to the left:

X+4X-(27/X+2X)=0


Domain of the equation: X+2X)!=0

X∈R


We add all the numbers together, and all the variables

X+4X-(+2X+27/X)=0

We add all the numbers together, and all the variables

5X-(+2X+27/X)=0

We get rid of parentheses

5X-2X-27/X=0

We multiply all the terms by the denominator


5X*X-2X*X-27=0

Wy multiply elements

5X^2-2X^2-27=0

We add all the numbers together, and all the variables

3X^2-27=0

a = 3; b = 0; c = -27;
Δ = b2-4ac
Δ = 02-4·3·(-27)
Δ = 324
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{324}=18$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-18}{2*3}=\frac{-18}{6}
=-3
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+18}{2*3}=\frac{18}{6}
=3
$