How do you solve the following linear system: $2x-y+3z= 7 , 5x-4y-2z= 3 , 4x+y-2z=-4$ ?

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Answer 1 · 2016-02-09T07:39:09

$x=17/81$
$y=-110/81$
$z=47/27$

Let $2x-y+3z=7$ 1st equation
Let $5x-4y-2z=3$ 2nd equation
Let $4x+y-2z=-4$ 3rd equation

Use 3rd equation so that $y$ in terms of $x$ and $z$

$y=-4+2z-4x$ 3rd equation

Use now 1st and 3rd
$2x-y+3z=7$ 1st equation
$2x-(-4+2z-4x)+3z=7$

$2x+4-2z+4x+3z=7$
$2x+4x-2z+3z=7-4$
$6x+z=3$ Let this be the 4th equation

Use 2nd and 3rd equations:

$5x-4y-2z=3$ 2nd equation

$5x-4(-4+2z-4x)-2z=3$
$5x+16-8z+16x-2z=3$
$5x+16x-8z-2z=3-16$
$21x-10z=-13$ Let this be the 5th equation

Solve for $x$ and $z$ using 4th and 5th equations

From 4th equation: $z=3-6x$ insert in 5th equation

$21x-10z=-13$ 5th equation

$21x-10(3-6x)=-13$

$21x-30+60x=-13$

$81x=30-13$
$81x=17$
$x=17/81$

Go back to the 4th equation , use $x=17/81$

From 4th equation: $z=3-6x$
$z=3-6*17/81$

$z=47/27$
Go back to the 3rd equation and use $x=17/81$ and $z=47/27$

$y=-4+2z-4x$ 3rd equation
$y=-4+2*47/27-4*17/81$
$y=-110/81$

The solution set:

$x=17/81$
$y=-110/81$
$z=47/27$

have a nice day from the Philippines!

How do you solve the following linear system: 2x-y+3z= 7 , 5x-4y-2z= 3 , 4x+y-2z=-4 2x-y+3z= 7 , 5x-4y-2z= 3 , 4x+y-2z=-4 ?