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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 2 and 3 that contain opposite coefficient of z - variable multiply the third equation by 3.
\Write the equations 2 and 3 in column form and add the corresponding columns to eliminate z - variable.
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The resultant equation is taken as fourth equation : 6x + 2y = 12.
\Solve the system of two equations with two variables.
\To get two equations 1 and 4 that contain opposite coefficient of x - variable multiply the first equation by negative 6.
\Write the equations 1 and 4 in column form and add the corresponding columns to eliminate x - variable.
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.
The resultant statement 20y = - 60 ------> y = - 3.
\To find the value of x, substitute y = - 3 in the equation 1 : x - 3y = 12 and solve for x.
\x - 3(- 3) = 12
\x + 9 = 12
\x = 3.
\To find the value of z, substitute x = 3 in the equation 3 : 2x + z = 7 and solve for z.
\2(3) + z = 7
\6 + z = 7
\z = 1.
\The solution (x, y, z) = (3, - 3, 1).