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

Aug 17, 2014

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:
$2 x + y = 4$
$2 x + y = - 3$

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 $0 x + 0 y = 7$.

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.