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.The system of equations are .
Use the elimination method to make a system of two equations in two variables.
\The two equations 1 and 2 contains opposite coefficient of z - variable.
\Write the equations 1 and 2 in column form and add the corresponding columns to eliminate z - variable.
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The resultant equation is taken as fourth equation : 3x + y = 10.
\The two equations 2 and 3 contains same coefficient of z - variable.
\Write the equations 2 and 3 in column form and subtract the corresponding columns to eliminate z - variable.
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The resultant equation is taken as fifth equation : 3x + 2y = 11.
\Solve the system of two equations with two variables.
\The two equations 4 and 5 contains same coefficient of x - variable.
\Write the equations 4 and 5 in column form and subtract the corresponding columns to eliminate x - variable.
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.
The resultant equation is - y = - 1 ----> y = 1.
\Use one of the equation with two variables (Equation: 4 or 5) to solve for x.
\The fourth equation: 3x + y = 10.
\3x + (1) = 10
\3x = 9
\x = 3.
\Solve for z using one of the original equations with three variables.
\The second equation: 2x - y + z = 7.
\2(3) - (1) + z = 7
\5 + z = 7
\z = 2.
\The solution (x, y, z) = (3, 1, 2).