Question

Find the solution to the system of equations.

3x + y + z = 6
3x - y + 2z=9
y+ Z=3
O A. x = 2, y=-1, z = 5
O B. x = 1, y = 0, z = 3
O C. x = 5, y = -2, z = 6
O D. x = 2, y = 1, z = 4

Answer 1

B. x = 1, y = 0, z = 3

Explanation:

Systems of linear equations are readily solved by a suitable calculator or spreadsheet. The attached calculator display shows the solution to be ...

x = 1, y = 0, z = 3

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There are several ways a calculator can solve these equations. The method shown here is to input the equations as an augmented matrix of their coefficients, and reduce it to row-echelon form. The right-most column of the reduced matrix is the set of variable values in the same order as the coefficients.

A graphing calculator can also be used to graph the equations. You may have to write one variable in terms of the others. (Here, it is convenient to let z=3-y.) The second attachment shows the solution (x, y) = (1, 0). This is sufficient to choose the correct answer. Or, you can finish the solution by substituting into the expression for z: z = 3 -y = 3 -0 = 3.

Many calculators will solve the system of equations after you enter it as presented in the problem statement.