# How do solve the following linear system?:  x+2y=1 , 9 x+ 16y =3 ?

$x = - 5$ and $y = 3$

#### Explanation:

Let $x + 2 y = 1$ the 1st equation
Let $9 x + 16 y = 3$ the 2nd equation

Use 1st into the 2nd equation

from 1st:
$x = 1 - 2 y$

using 2nd:
$9 x + 16 y = 3$

$9 \left(1 - 2 y\right) + 16 y = 3$

$9 - 18 y + 16 y = 3$

$- 2 y = - 6$

$\frac{\cancel{- 2} y}{\cancel{- 2}} = \frac{- 6}{-} 2$

and $y = 3$

Go back to the 1st equation and use $y = 3$

$x = 1 - 2 y$
$x = 1 - 2 \cdot 3$
$x = 1 - 6$
$x = - 5$

have a nice day from the Philippines!