Home > Precalculus > Solving a System of Equations Using a Matrix

How do I use matrices to find the solution of the system of equations #y=−2x+4# and #y=−2x−3#?

Answer 1

This system is inconsistent meaning there is no solution.

You need to move all the variables to the left of the equals sign and put them in alphabetical order: #2x+y=4# #2x+y=-3#

Then put them in matrix form: [2 1 | 4] [2 1 | -3]

Then perform your reduction (R2 = R1-R2): [2 1 | 4] [0 0 | 7]

The second row tells you the system is inconsistent because you have #0x+0y=7#.

Remember that solving with matrices is no different than solving using variables; you are simply leaving out the variables to save time.

You can also enter the matrix into a calculator and solve using "rref" on the TI-83/84 or the Casio fx-9750/9860.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.