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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 x - variable multiply the second equation by 2.
\Write the equations 2 and 3 in column form and add the corresponding columns to eliminate x - variable.
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The resultant equation is taken as fourth equation : 6y +3z = 9.
\Solve the system of two equations with two variables.
\To get two equations 1 and 4 that contain opposite coefficient of z - variable multiply the first equation by 3.
\Write the equations 1 and 4 in column form and add the corresponding columns to eliminate z - variable.
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The resultant equation 12y = 0 ------> y = 0.
\To find the value of z, substitute y = 0 in the equation 1 : 2y - z = - 3 and solve for x.
\2(0) - z = - 3
\- z = - 3 \ \
\z = 3.
\To find the value of x, substitute y = 0 in the equation 2 : - 2x + 3y = 10 and solve for x.
\- 2x + 3(0) = 10
\- 2x = 10
\x = - 5.
\The solution (x, y, z) = (- 5, 0, 3).