How do you solve the following system: -3y + x = -3, -5x − y = 14 ?

May 15, 2018

color(green)(x= -2(13/16), y = 1/16

Explanation:

$x - 3 y = - 3$, Eqn (1)

$- 5 x - y = 14$, Eqn (2)#

5 * Eqn(1) + Eqn (2) is

$5 x - 15 y - 5 x - y = - 15 + 14$

$- 16 y = - 1$

$y = \frac{1}{16}$

Substituting value of y in Eqn (1),

$x - \frac{3}{16} = - 3$

$x = - 3 + \frac{3}{16} = - 2 \left(\frac{13}{16}\right)$

May 15, 2018

$x = - \frac{45}{16}$ , or $- 2.8125$
$y$ = $\frac{1}{16}$

Explanation:

Here's our system:

$- 3 y + x = - 3$
$- 5 x - y = 14$

Solving By Substitution

First, let's solve for a variable. I'll choose x, since it appears first. We'll solve for x by using the first equation:

$- 3 y + x = - 3$

Add 3y to both sides in order to negate -3y. You should now have:

$x = 3 y - 3$

Now, substitute this value in the second equation:

$- 5 \left(3 y - 3\right) - y = 14$

Distribute -5 to all terms in the parentheses. Remember negative and positive multiplication rules. (Two negatives make a positive!)

$- 15 y + 15 - y = 14$

Now, combine like terms.

$- 16 y + 15 = 14$

Now, subtract 15 from both sides in order to solve for y.

$- 16 y = - 1$

Now, divide by $- 16$ to isolate for $y$.

$- \frac{1}{-} 16$ = $y$

Because two negatives make a positive, $y$ becomes $\frac{1}{16}$.

Now, plug y in the simplified equation used to solve for x earlier:

$x = 3 y - 3$

Substitute $y$ for $y$'s value.

$x = 3 \left(\frac{1}{16}\right) - 3$

Multiply 3 by 1/16 to get 3/16.

$x = \left(\frac{3}{16}\right) - 3$

$x = - \frac{45}{16}$ , or $- 2.8125$