# How do you solve the following system: 5x+8y= -29 , x+3y=3 ?

Mar 6, 2016

The solution for the system of equations is:
color(green)(x=-111/7

color(green)(y =44/7

#### Explanation:

$\textcolor{g r e e n}{5 x} + 8 y = - 29$.............equation $\left(1\right)$

$x + 3 y = 3$, multiplying by $5$
$\textcolor{g r e e n}{5 x} + 15 y = 15$.................equation $\left(2\right)$

Solving by elimination:
Subtracting equation $2$ from $1$ would eliminate $\textcolor{g r e e n}{5 x}$

$\cancel{\textcolor{g r e e n}{5 x}} + 8 y = - 29$
$- \cancel{\textcolor{g r e e n}{5 x}} - 15 y = - 15$

$- 7 y = - 34$

$y = \frac{- 44}{- 7}$

color(green)(y =44/7

Finding $x$ from equation $2$:

$\textcolor{g r e e n}{5 x} + 15 y = 15$

$5 x = 15 - 15 y$

$5 x = 15 - 15 \times \left(\frac{44}{7}\right)$

$5 x = 15 - \left(\frac{660}{7}\right)$

$5 x = \frac{105}{7} - \left(\frac{660}{7}\right)$

$5 x = \left(- \frac{555}{7}\right)$

$x = \left(- \frac{555}{7 \times 5}\right)$

color(green)(x=-111/7

$x = - \frac{111}{7}$
$y = \frac{44}{7}$

#### Explanation:

From the given equations
$5 x + 8 y = - 29 \text{ }$first equation
$x + 3 y = 3 \text{ }$second equation

Let $x = 3 - 3 y$ substitute in the first equation

$5 x + 8 y = - 29 \text{ }$first equation
$5 \left(3 - 3 y\right) + 8 y = - 29 \text{ }$
$15 - 15 y + 8 y = - 29$
$- 7 y = - 29 - 15$
$- 7 y = - 44$
$y = \frac{44}{7}$

Use $y = \frac{44}{7}$ in the second equation

$x = 3 - 3 y$
$x = 3 - 3 \left(\frac{44}{7}\right)$
$x = \frac{21 - 132}{7}$
$x = - \frac{111}{7}$

checking
$5 x + 8 y = - 29 \text{ }$first equation
$5 \left(- \frac{111}{7}\right) + 8 \left(\frac{44}{7}\right) = - 29 \text{ }$

$- \frac{555}{7} + \frac{352}{7} = - 29$
$- \frac{203}{7} = - 29$
$- 29 = - 29$

checking
$x + 3 y = 3 \text{ }$second equation
$\left(- \frac{111}{7}\right) + 3 \left(\frac{44}{7}\right) = 3 \text{ }$
$- \frac{111}{7} + \frac{132}{7} = 3$
$\frac{21}{7} = 3$
$3 = 3$

God bless....I hope the explanation is useful..