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

1 Answer
radee
Feb 4, 2016

(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)

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