How do you solve the following linear system: # x + y = 6 , x = y + 2 #?

1 Answer
Eivind K.
Nov 19, 2015

Substitute #x# by using #y# or vice versa.
Solve it like a normal equation
Solve for the other variable

Explanation:

#1: x + y = 6#
#2: x = y + 2#

The second equation helps us a lot here, since #x# is isolated from #y# and the constant. The second equation states that #x# can be written as #y + 2#, since #x = y + 2#. Put this expression into equation number 1.

#1: color(red)(y + 2) + y = 6#
NOTE: The red symbolizes a #x#.

#1: 2y = 6 - 2#
#1: 2y = 4#
#1: y = 2#

Put the value of #y# into the first equation.
#x + y = 6#
#x + 2 = 6#
#x = 6 - 2#
#x = 4#

Conclusion: #x = 4# and #y=2#

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