# Math Help - systems of equations

1. ## systems of equations

xy + xz = -1
xy + yz = -9
yz + xz = -4

solve for (x,y,z)

2. Originally Posted by stasis
xy + xz = -1
xy + yz = -9
yz + xz = -4

solve for (x,y,z)
I'd suggest substituting xy = a, xz = b and yz = c. Solve the three new linear equations simultaneously for a, b and c. NOw use these values to solve for x, y and z.

By the way ..... There are several good reasons NOT delete questions once they've been answered. (I refer to your edit at http://www.mathhelpforum.com/math-he...-question.html)

3. Originally Posted by stasis

xy + xz = -1 (1)
xy + yz = -9 (2)
yz + xz = -4 (3)

solve for (x,y,z)
Hello Stasis. This problem can easily be solved by doing some basic elimination and substitution.

My approach starts with (1) - (2) to give $xz -yz = 8$ call this (4)

then (3) + (4) give $2xz = 4 \ \ \Rightarrow \ \ xz = 2$
substitute $xz = 2$ into (1) and (3) to get $yz=-6$ and $xy = -3$

so we have:
$xz = 2 \ \ \ \ \ \ (5)$
$yz=-6 \ \ \ \ (6)$
$xy = -3 \ \ \ \ (7)$

now (7)*(5) gives $x^2yz = -6$ (6) gives $yz=-6$ therefore $x^2 = 1 \ \ \Rightarrow \ \ x = \pm 1$

putting $x = \pm 1$ in (5) gives $z = \pm 2$
and into (7) $y = \mp 3$

so your two solutions are $( \pm 1 , \mp 3 , \pm 2 )$

Bobak