Solve the system. {:[x+3y-z=,-6],[-2x-y+z=,10],[x-y+3z=,2]:}

Question

Solve the system.  {:[x+3y-z=,-6],[-2x-y+z=,10],[x-y+3z=,2]:}

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Write Equations: Write down the system of equations. The system of equations is: x + 3y - z = -6 -2x - y + z = 10 x - y + 3z = 2Elimination Method: Use the elimination method to eliminate one variable. We can start by eliminating the variable z. To do this, we can add the first and second equations to eliminate z. (x + 3y - z) + (-2x - y + z) = -6 + 10 This simplifies to: -x + 2y = 4Solve for x and y: Now we have a new system of two equations with two variables. The new system is: -x + 2y = 4 x - y + 3z = 2Equations with y and z: Solve the new system for x and y. We can solve for x from the first equation of the new system: -x + 2y = 4 x = 2y - 4 Now we substitute x in the second equation: (2y - 4) - y + 3z = 2 y - 4 + 3z = 2 y + 3z = 6Solve for y and z: We now have two equations with y and z. The equations are: y + 3z = 6 -2x - y + z = 10 We can substitute x from step 4 into the second equation: -2(2y - 4) - y + z = 10 -4y + 8 - y + z = 10 -5y + z = 2Find z: Solve the system of equations with y and z. We have two equations: y + 3z = 6 -5y + z = 2 We can multiply the first equation by 5 to eliminate y: 5(y + 3z) = 5(6) 5y + 15z = 30 Now we add this to the second equation: 5y + 15z + (-5y + z) = 30 + 2 This simplifies to: 16z = 32 z = 32 / 16 z = 2Find y: Substitute z back into one of the equations to find y. We can use the equation y + 3z = 6: y + 3(2) = 6 y + 6 = 6 y = 6 - 6 y = 0Find x: Substitute y back into the equation from step 4 to find x. We use the equation x = 2y - 4: x = 2(0) - 4 x = -4Final Solution: Write down the solution to the system of equations. The solution is x = -4, y = 0, z = 2.

Solve the system. $\newline$ $\begin{cases} x+3y-z&=-6 \ -2x-y+z&=10 \ x-y+3z&=2 \end{cases}$

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Solve the system.\newline{x+3y−zamp;=−6 −2x−y+zamp;=10 x−y+3zamp;=2\begin{cases} x+3y-z&amp;=-6 \ -2x-y+z&amp;=10 \ x-y+3z&amp;=2 \end{cases}{x+3y−z​amp;=−6 −2x−y+z​amp;=10 x−y+3z​amp;=2​

Solve the system. $\newline$ $\begin{cases} x+3y-z&=-6 \ -2x-y+z&=10 \ x-y+3z&=2 \end{cases}$