Question

1. Solve the given system of equations. X + y + z = 9 x - z = 5 X + y = 6the solution is: x = y = and z =

Answer 1

x=8

y=-2

Z=3

Step-by-step explanation

Step 1

Let

`\begin{gathered} x+y+z=9\text{ Equation (1)} \\ x-z=5\text{ Equation(2)} \\ x+y=6\text{ Equation(3)} \end{gathered}`

Step 2

isolate x from equation (1) , (2) and (3)

`\begin{gathered} x+y+z=9 \\ x=9-y-z\text{ Equation (4)} \end{gathered}`

`\begin{gathered} x-z=5 \\ x=5+z\text{ equation (5)} \\ \\ x+y=6 \\ x=6-y\text{ equation(6)} \\ \end{gathered}`

Step 3

combining equation (4) and (5)

`\begin{gathered} 9-y-z=5+z \\ 9-y-2z=5 \\ -y-2z=5-9 \\ -y-2z=-4\text{ Equation(7)} \end{gathered}`

Step 4

`\begin{gathered} x=x \\ \text{equation (5) = equation (6)} \\ 5+z=6-y\text{ equation (8)} \end{gathered}`

Step 5

using equation(7) and (8) find y and z

`\begin{gathered} -y-2z=-4\text{ (7)} \\ 5+z=6-y(8) \\ \text{isolate y from equation (7)} \\ -y=-4+2z \\ y=4-2z \\ \text{replace in equation (8)} \\ 5+z=6-4+2z \\ 5+z=2+2z \\ z-2z=2-5 \\ -z=-3 \\ z=3 \end{gathered}`

replace the value of z= 3 in equation (7) to find y

`\begin{gathered} -y-2z=-4 \\ -y-2\cdot3=-4 \\ -y-6=-4 \\ -6+4=y \\ y=-2 \end{gathered}`

finally, replace the value of y in equation (3) to find x

`\begin{gathered} x+y=6 \\ x-2=6 \\ x=6+2 \\ x=8 \end{gathered}`

I hope this helps you