How do solve the following linear system?: # x-4y=2 , 2x+6y=5 #?

1 Answer
Feb 17, 2016

Answer:

#(16/7, 1/14)#

Explanation:

In order to solve systems of linear equations, you can either use the

  1. Elimination Method
  2. Substitution Method
  3. Graphing

In this case, I would use the elimination method but note that you may use any method that you are comfortable with and still arrive at the same answer.

[Solution]
#x - 4y = 2#
#2x + 6y = 5#

Multiply 2 to both sides of the first equation...

#2x - 8y = 4#

Doing this makes the coefficient of x in the two equations the same. This enables us to subtract one equation from the other to eliminate the #x# variable

[Subtracting one equation from the other]
#2x + 6y = 5#
#2x - 8y = 4#

#14y = 1#
#y = 1/14#

Now that we know the value of #y#, we can now evaluate any of the two equations with the value of #y# to get the value of #x#

#x - 4(1/14) = 2#
#x - 2/7 = 2#
#x = 2 + 2/7#
#x = 16/7#

[Checking]
Substituting to equation 1 -> #x - 4y = 2#
#16/7 - 4(1/14) = 2#
#16/7 - 2/7 = 2#
#14/7 = 2#
#2 = 2#

Substituting to equation 2 -> #2x + 6y = 5#
#2(16/7) + 6(1/14) = 5#
#32/7 + 3/7 = 5#
#35/7 = 5#
#5 = 5#

[Final Answer]
#(16/7, 1/14)#