How do you solve 3x + y = -26 and 2x - y = -19?

1 Answer

Answer:

#x = -9# and #y = 1#

Explanation:

Using the method of simultaneous equations, you take the first equation and write #y# in terms of #x# to get

#y=-3x-26#

Then you substitute this into the second equation, ie. wherever you see a #y# in the second equation, you replace it with #(-3x-26)#. This yields

#2x-(-3x-26)=-19#

This then leaves an equation with only one unknown, #x#, so we may solve or #x# to obtain

#5x+26=-19 #

Therefore #x = - 9#.

Then substitute back to get the value or #y# as

#-3 * (-9) -26 = 1#

An alternative method would be to use linear matrix algebra, in which a separate 3 methods exist :

  • Gauss-Jordan elimination
  • Inverse matrix method
  • Kramer's Rule

Please let me know if you require me to resolve the problem using any of these 3 methods and I will do so for you, otherwise the simultaneous equation method shown above should suffice or a #2 xx 2# linear system. The matrix methods are more time efficient for higher order systems like #3 xx 3# and higher.