How do you solve the following system: #6x + y = 2, 4x + 7y = 6x#?

1 Answer
Feb 4, 2016

Answer:

#(7/22, 1/11)#

Explanation:

In order to solve systems of linear equations, you must first simplify your equations (combine all terms in the equation with the same variable).

#6x + y = 2#
#4x + 7y = 6x#

[Simplifying the 2nd equation]
#4x + 7y = 6x#
#2x - 7y = 0#

Now, you can choose whether to use the substitution method or elimination. Its up to you to choose which one you are more comfortable with but for now I will be using substitution since the #y# variable in the 1st equation has a coefficient of 1.

[Rearranging 1st Eqtn to isolate #y#]
#6x + y = 2#
#y = 2 - 6x#

[Substituting it to the 2nd equation]
#2x - 7y = 0#
#2x - 7(2 - 6x) = 0#
#2x - 14 + 42x = 0#
#44x - 14 = 0#
#44x = 14#
#x = 14/44#
#x = 7/22#

[Solving for #y#]
#y = 2 - 6(7/22)#
#y = 2 - 21/11#
#y = 1/11#

So the final answer is #(7/22, 1/11)#