Question

Solve the system of equations.

4x-3y+z = 18

x+y = 7

Select the correct choice below and, if necessary, fill in the answer boxes to complete your choice.

A. This system has exactly one solution. The solution is left parenthesis nothing comma nothing comma nothing right parenthesis . (Type integers or simplified fractions.)

B. This system has infinitely many solutions of the form left parenthesis nothing comma nothing comma z right parenthesis , where z is any real number. (Type expressions using z as the variable. Use integers or fractions for any numbers in the expressions.)

C. This solution has no solution.

Answer 1

For unique solution, number of equations required will be equal to the number of variables.

Since there are two equations and variable are three, therefore there will not be a unique solution.

For any particular value of z, there will be two equations in x and y which can be solved to find unique value of x and y.

Since the value of z can be any real number, therefore there will be infinite many solution which can be represented as ( , , z).

Hence the option (B) is correct.