Question

solve the following system of equations for all three variables.
2x + 6y + z = -6
6x - 5y - z = -2
4x + 4y + z = -8
answer attempt 1 out of 2
x =
y =
z =
submit answer

Explanation:

Step1: Add first and second equations

\[

$$\begin{align*} (2x + 6y+z)+(6x - 5y - z)&=-6+( - 2)\\ 2x+6x+6y - 5y+z - z&=-8\\ 8x + y&=-8 \quad(1) \end{align*}$$

\]

Step2: Subtract third equation from first equation

\[

$$\begin{align*} (2x + 6y+z)-(4x + 4y + z)&=-6-( - 8)\\ 2x-4x+6y - 4y+z - z&=2\\ -2x+2y&=2\\ -x + y&=1 \quad(2) \end{align*}$$

\]

Step3: Subtract equation (2) from equation (1)

\[

$$\begin{align*} (8x + y)-(-x + y)&=-8 - 1\\ 8x+x+y - y&=-9\\ 9x&=-9\\ x&=-1 \end{align*}$$

\]

Step4: Substitute \(x = - 1\) into equation (2)

\[

$$\begin{align*} -(-1)+y&=1\\ 1 + y&=1\\ y&=0 \end{align*}$$

\]

Step5: Substitute \(x=-1\) and \(y = 0\) into the first equation

\[

$$\begin{align*} 2(-1)+6(0)+z&=-6\\ -2+z&=-6\\ z&=-4 \end{align*}$$

\]

Answer:

\(x=-1,y = 0,z=-4\)