Solving a System of Equations with a MatrixAlgebra I

Steps:• Put the two equations in standard form, so that the

x – terms are in a column, the y – terms are in a column, and the constants are in a column.

• Re-write the equations with out the variables or the equals symbol to form an augmented matrix

• Type the matrix in the calc. Press “2nd” “Matrix” got to Edit enter the matrix and go back to the home screen.

• Press “2nd” “Matrix” Math scroll down to “B: rref” then press “2nd” “Matrix” then scroll down to matrix you entered press “Enter” twice.

• Copy the new matrix onto your paper.• Write out the answer.

Answer decoding

•Answer form: 1 0 x (One Solution)0 1 y (x,y) is the

solution

•Answer form: 1 0 0 (Infinitely Many0 0 0 Solutions)

•Answer form: 1 0 0 (No Solutions)0 0 # # is any number

but 0

Example

•Solve: y = -3x + 2-2x = -y – 4

•Solution: (6/5, -8/5)

Example

•Solve: 2x + y = -4x + 1/2y = -2

•Solution: Infinitely Many Solutions

Example:

•Solve: 4x – y = 118x – 2y = 15

•Solution: No Solutions