Question

What is the solution of the system of equations negative 3x - 4y - 3z equals -7 2 x - 6 y + 2 Z equals 3 5 x - 2 y + 5 Z equals 9

Answer 1

The solution of the system of equations negative 3x - 4y - 3z equals -7 2 x - 6 y + 2 Z equals 3 5 x - 2 y + 5 Z equals 9(x, y, z) is $\left(\frac{-1}{6}, \frac{3}{26}, \frac{157}{78}\right)$

Solution:

Given, system of equations are  

3x – 4y – 3z = - 7 ----- eqn (1)

2x – 6y + 2z = 3 ------ eqn (2)

5x – 2y + 5z = 9 ---- eqn (3)

We have to find the solution of the equations.

Now, from eqn (2)

$x-3 y+z=\frac{3}{2}$   ----- eqn 4

Multiply eqn 4 with 5

$5 x-15 y+5 z=\frac{15}{2}$

Now subtract eqn 5 from eqn 3

5x – 2y + 5z = 9

5x – 15y + 5z = 15/2

(-)-----------------------------------

0 + 13y + 0 = 9 - 15/2

$\begin{array}{l}{13 y=\frac{18-15}{2}} \\\\ {y=\frac{3}{26}}\end{array}$

Now, perform eqn (1) + 3 x eqn (1)

3x – 4y – 3z = - 7  

3x – 9y + 3z = 9/2

(+) -------------------------------------

6x – 13y = - 7 + 9/2  

$\begin{array}{l}{6 x-13 \times \frac{3}{26}=\frac{9-14}{2}} \\\\ {6 x-\frac{3}{2}=\frac{-5}{2}} \\\\ {6 x=-1} \\\\ {x=\frac{-1}{6}}\end{array}$

Then from eqn (4)

$\begin{array}{l}{\frac{-1}{6}-3 \times \frac{3}{26}+z=\frac{3}{2}} \\\\ {z=\frac{3}{2}+\frac{9}{26}+\frac{1}{6}} \\\\ {z=\frac{39+9}{26}+\frac{1}{6}} \\\\ {z=\frac{48}{26}+\frac{1}{6}} \\\\ {z=\frac{24}{13}+\frac{1}{6}=\frac{157}{78}}\end{array}$

Hence, the solution is (x, y, z) is $\left(\frac{-1}{6}, \frac{3}{26}, \frac{157}{78}\right)$