How do you solve the system of equations algebraically 1.8x-z=0.7, 1.2y+z=-0.7, 1.5x-3y=3?

Dec 30, 2016

$x = 0.5$, $y = - 0.75$ and $z = 0.2$

Explanation:

The three equations are

$1.8 x - z = 0.7$ ...........................(1)

$1.2 y + z = - 0.7$ ...........................(2)

$1.5 x - 3 y = 3$ ...........................(3)

Note that adding (1) and (2) eliminates $z$ and we get

$1.8 x + 1.2 y = 0$ ...........................(4)

Now multiplying (3) by $6$ and (4) by $5$, we get

$9 x - 18 y = 18$ and $9 x + 6 y = 0$ and subtracting latter from former, we get $- 18 y - 6 y = 18 - 0$ i.e. $- 24 y = 18$

Hence $y = - \frac{18}{24} = - 0.75$.

Putting this in (3) we get

$1.5 x - 3 \times \left(- 0.75\right) = 3$ or $1.5 x = 3 - 2.25 = 0.75$

Hence $x = \frac{0.75}{1.5} = 0.5$

Now putting this in (1) , we get

$1.8 \times 0.5 - z = 0.7$ or $0.9 - z = 0.7$ i.e.

$z = 0.9 - 0.7 = 0.2$

Hence solution is $x = 0.5$, $y = - 0.75$ and $z = 0.2$