# How do solve the following linear system?:  4x+y=6 , 7x-2y=-16 ?

Feb 22, 2016

Solution is $x = - \frac{4}{15}$ and $y = \frac{106}{15} = 7 \frac{1}{15}$

#### Explanation:

For solving system of linear equations $4 x + y = 6$ and 7x−2y=−16, what is required is first eliminating one variable to get the value of another and then substituting second in either to get value of first variable.

For this, let us choose and get $y$ from first equation $4 x + y = 6$, which gives, $y = 6 - 4 x$.

Now putting this in second equation 7x−2y=−16, we get

$7 x - 2 \left(6 - 4 x\right) = - 16$ or $7 x - 12 + 8 x = - 16$ or

$15 x = 12 - 16 = - 4$. Hence $x = - \frac{4}{15}$

Hence $y = 6 - 4 \cdot \left(- \frac{4}{15}\right)$ or $y = 6 + \frac{16}{15} = \frac{106}{15}$

Hence solution is $x = - \frac{4}{15}$ and $y = \frac{106}{15} = 7 \frac{1}{15}$