# How do solve the following linear system?:  x+2y=1 , -3x -8y = -9 ?

May 1, 2017

x=-5 and y=3

#### Explanation:

$x + 2 y = 1$
$x = 1 - 2 y$ -----(1)

$- 3 x - 8 y = - 9$
$3 x + 8 y = 9$ -----(2)

Substituting (1) into (2):

$3 \left(1 - 2 y\right) + 8 y = 9$
$2 y + 3 = 9$
$y = 3$

Substituting y=3 into (1):

$x = 1 - 2 \left(3\right) = - 5$

May 1, 2017

See the entire solution process below:

#### Explanation:

Step 1) Solve the first equation for $x$:

$x + 2 y = 1$

$x + 2 y - \textcolor{red}{2 y} = 1 - \textcolor{red}{2 y}$

$x + 0 = 1 - 2 y$

$x = 1 - 2 y$

Step 2) Subsitute $1 - 2 y$ for $x$ in the second equation and solve for $y$:

$- 3 x - 8 y = - 9$ becomes:

$- 3 \left(1 - 2 y\right) - 8 y = - 9$

$\left(- 3 \cdot 1\right) - \left(- 3 \cdot 2 y\right) - 8 y = - 9$

$- 3 - \left(- 6 y\right) - 8 y = - 9$

$- 3 + 6 y - 8 y = - 9$

$- 3 + \left(6 - 8\right) y = - 9$

$- 3 - 2 y = - 9$

$\textcolor{red}{3} - 3 - 2 y = \textcolor{red}{3} - 9$

$0 - 2 y = - 6$

$- 2 y = - 6$

$\frac{- 2 y}{\textcolor{red}{- 2}} = - \frac{6}{\textcolor{red}{- 2}}$

$\frac{\textcolor{red}{\cancel{\textcolor{b l a c k}{- 2}}} y}{\cancel{\textcolor{red}{- 2}}} = 3$

$y = 3$

Step 3) Substitute $3$ for $y$ in the solution to the first equation at the end of Step 1 and calculate $x$:

$x = 1 - 2 y$ becomes:

$x = 1 - \left(2 \cdot 3\right)$

$x = 1 - 6$

$x = - 5$

The solution is: $x = - 5$ and $y = 3$ or $\left(- 5 , 3\right)$