# How do you solve the system 3x+2y=-17 and 2x-5y=14 by substitution?

Mar 10, 2018

$x = - 3 \mathmr{and} y = - 4$

#### Explanation:

Substitution would certainly not be my method of choice for this example, but here goes...

You need to have one of the equations with $x$ or $y$ as the subject, ie as a single variable,

$2 x - 5 y = 14$ can be written as $\textcolor{b l u e}{x = \frac{5 y + 14}{2}}$

Now substitute that expression for $x$ in the other equation:

$3 \textcolor{b l u e}{x} + 2 y = - 17$

3color(blue)(((5y+14)/2)) +2y =-17: "larr now solve for $y$

$3 \left(5 y + 14\right) + 4 y = - 34 \text{ } \leftarrow \times 2$

$15 y + 42 + 4 y = - 34$

$19 y = - 34 - 42$

$19 y = - 76$

$y = - 4$

Now find $x$ by substituting $y = - 4$

$\textcolor{b l u e}{x = \frac{5 \left(- 4\right) + 14}{2}}$

$x = - 3$

Check:

$3 x + 2 y$

$= 3 \left(- 3\right) + 2 \left(- 4\right)$

$- 9 - 8$

$= - 17$

Mar 10, 2018

$y = - 4 , x = - 3$

#### Explanation:

$3 x + 2 y = - 17 - - - - - - \left(1\right)$

$2 x - 5 y = 14 - - - - - - - \left(2\right)$

$\left(1\right) \times 2 : -$

$\therefore 6 x + 4 y = - 34 - - - - - - \left(3\right)$

$\left(2\right) \times 3 : -$

$\therefore 6 x - 15 y = 42 - - - - - - \left(4\right)$

$\left(3\right) - \left(4\right) : -$

$\therefore 19 y = - 76$

$\therefore y = - 4$

substitute $y = - 4$ in (1)#

$\therefore 3 x + 2 \left(- 4\right) = - 17$

$\therefore 3 x - 8 = - 17$

$\therefore 3 x = - 17 + 8$

$\therefore 3 x = - 9$

$\therefore x = - \frac{9}{3}$

$\therefore x = - 3$
~~~~~~~~~~~~~~
substitute $y = - 4 , x = - 3$ in (2)

$\therefore 2 \left(- 3\right) - 5 \left(- 4\right) = 14$

$\therefore - 6 + 20 = 14$

$\therefore 14 = 14$