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

2 Answers
May 15, 2018

Answer:

#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

Answer:

#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#