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

Feb 4, 2016

$\left(\frac{7}{22} , \frac{1}{11}\right)$

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).

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

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

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 $y$]
$6 x + y = 2$
$y = 2 - 6 x$

[Substituting it to the 2nd equation]
$2 x - 7 y = 0$
$2 x - 7 \left(2 - 6 x\right) = 0$
$2 x - 14 + 42 x = 0$
$44 x - 14 = 0$
$44 x = 14$
$x = \frac{14}{44}$
$x = \frac{7}{22}$

[Solving for $y$]
$y = 2 - 6 \left(\frac{7}{22}\right)$
$y = 2 - \frac{21}{11}$
$y = \frac{1}{11}$

So the final answer is $\left(\frac{7}{22} , \frac{1}{11}\right)$