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

Mar 30, 2018

$x = \frac{4}{19}$ and $y = \frac{14}{19}$

#### Explanation:

We will do the elimination method. First multiply first equation by 3 and second equation by 2 so we would have

$12 x + 21 y = 18$

$12 x + 2 y \setminus \setminus = 4$

Subtract first equation by second equation to obtain $19 y = 14$

So $y = \frac{14}{19}$

Now plug the value of y into second equation and solve for x:

$6 x + \frac{14}{19} = 2$

$6 x = \frac{24}{19}$

$x = \frac{24}{6 \cdot 19} = \frac{4}{19}$

So the solution is $x = \frac{4}{19}$ and $y = \frac{14}{19}$