What is the solution to this system of equations? {[x+3y-z=6],[4x-2y+2z=-10],[6x+z=-12]:}

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What is the solution to this system of equations?  {[x+3y-z=6],[4x-2y+2z=-10],[6x+z=-12]:}

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Write Equations: Write down the system of equations to be solved. {[x+3y-z=6],[4x-2y+2z=-10],[6x+z=-12]:} We need to find the values of x, y, and z that satisfy all three equations simultaneously.Eliminate Variable z: Choose two equations to eliminate one variable. We can start by eliminating z using the first and third equations. First equation: x + 3y - z = 6 Third equation: 6x + z = -12 Add the first and third equations to eliminate z: (x + 3y - z) + (6x + z) = 6 - 12 7x + 3y = -6Eliminate Variable z: Now, we need to eliminate the same variable, z, using the second and third equations. Second equation: 4x - 2y + 2z = -10 Third equation: 6x + z = -12 To eliminate z, we can multiply the third equation by 2 and then add it to the second equation: (4x - 2y + 2z) + 2*(6x + z) = -10 + 2*(-12) 4x - 2y + 2z + 12x + 2z = -10 - 24 16x - 2y + 4z = -34 Now, we divide the entire equation by 2 to simplify: (16x - 2y + 4z)/2 = -34/2 8x - y + 2z = -17Two-Variable Equations: We now have two equations with two variables (x and y): 7x + 3y = -6 8x - y = -17 We can multiply the second equation by 3 to align the y terms: 3*(8x - y) = 3*(-17) 24x - 3y = -51 Now we can add this result to the first equation to eliminate y: (7x + 3y) + (24x - 3y) = -6 + (-51) 31x = -57 Divide both sides by 31 to solve for x: x = -57 / 31 x = -1.8387 (rounded to four decimal places)Solve for x: Substitute the value of x into one of the two-variable equations to solve for y. We can use the equation 8x - y = -17: 8(-1.8387) - y = -17 -14.7096 - y = -17 Add 14.7096 to both sides to solve for y: -y = -17 + 14.7096 -y = -2.2904 Multiply both sides by -1: y = 2.2904 (rounded to four decimal places)Solve for y: Substitute the values of x and y into one of the original equations to solve for z. We can use the first equation x + 3y - z = 6: -1.8387 + 3(2.2904) - z = 6 -1.8387 + 6.8712 - z = 6 4.0325 - z = 6 Subtract 4.0325 from both sides to solve for z: -z = 6 - 4.0325 -z = 1.9675 Multiply both sides by -1: z = -1.9675 (rounded to four decimal places)

What is the solution to this system of equations? $\newline$ $\left\{\begin{array}{c} x+3 y-z=6 \\ 4 x-2 y+2 z=-10 \\ 6 x+z=-12 \end{array}\right.$

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What is the solution to this system of equations?\newline{x+3y−z=64x−2y+2z=−106x+z=−12 \left\{\begin{array}{c} x+3 y-z=6 \\ 4 x-2 y+2 z=-10 \\ 6 x+z=-12 \end{array}\right. ⎩⎨⎧​x+3y−z=64x−2y+2z=−106x+z=−12​

What is the solution to this system of equations? $\newline$ $\left\{\begin{array}{c} x+3 y-z=6 \\ 4 x-2 y+2 z=-10 \\ 6 x+z=-12 \end{array}\right.$