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

2 Answers
May 15, 2018

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

Explanation:

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

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

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

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

-16y = -1

y = 1/16

Substituting value of y in Eqn (1),

x - 3/16 = -3

x = -3 + 3/16 = -2(13/16)

May 15, 2018

x = -45/16 , or -2.8125
y = 1/16

Explanation:

Here's our system:

-3y + x = -3
-5x - 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:

-3y + x = -3

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

x = 3y - 3

Now, substitute this value in the second equation:

-5(3y - 3) - y = 14

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

-15y + 15 - y = 14

Now, combine like terms.

-16y + 15 = 14

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

-16y = -1

Now, divide by -16 to isolate for y.

-1/-16 = y

Because two negatives make a positive, y becomes 1/16.

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

x = 3y -3

Substitute y for y's value.

x = 3(1/16) - 3

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

x = (3/16) - 3

x = -45/16 , or -2.8125