Question

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

Answer 1

`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)`

Answer 2

`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`