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.The system of equations are .
Use the elimination method to make a system of two equations in two variables.
\To get two equations 1 and 2 that contain opposite coefficient of y - variable multiply the first equation by 3.
\Write the equations 1 and 2 in column form and add the corresponding columns to eliminate y - variable.
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The resultant equation is taken as fourth equation : 4x + 4z = 6.
\To get two equations 2 and 3 that contain opposite coefficient of y - variable multiply the third equation by 3.
\Write the equations 2 and 3 in column form and add the corresponding columns to eliminate y - variable.
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The resultant equation is taken as fifth equation : 10x + 16z = 24.
\Solve the system of two equations with two variables.
\To get two equations 4 and 5 that contain opposite coefficient of z - variable multiply the fourth equation by negative 4.
\Write the equations 4 and 5 in column form and add the corresponding columns to eliminate z - variable.
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The resultant statement - 6x = 0 ------> x = 0.
\Use one of the equation with two variables (Equation: 4 or 5) to solve for z.
\The fourth equation: 4x + 4z = 6.
\4(0) + 4z = 6
\4z = 6
\z = 6/4 = 3/2.
\Solve for y using one of the original equations with three variables.
\The first equation: 2x - y + 2z = 1.
\2(0) - y + 2(3/2) = 1
\- y + 3 = 1
\- y = - 2
\y = 2.
\The solution (x, y, z) = (0, 2, 3/2).