How do you solve #3x + y = 7# and #3x - y = 5#?

1 Answer
Jun 7, 2016

Answer:

#x = 2 " and " y = 1#

Explanation:

There are 2 obvious methods which can be used in this example, based on the x and y values in the equations.

ELIMINATION METHOD
The two y terms are additive inverses. This means they have the same value, but opposite signs.
When they are ADDED together, they will make 0.

#" " 3x + y = 7 " A"#
#" " 3x - y = 5 " B"#

#"A + B: " 6x " "= 12" (the y's have been eliminated)" #
#" " x" " = 2#

Substitute into A to find the value of y:
#" " 3(2) + y = 7#
#" " 6 + y = 7#
#" " y = 1#

EQUATING METHOD

The two x-terms are exactly the same. Make the x term the subject.

# 3x + y = 7 " and " 3x - y = 5#
#3x " " = 7 - y " " 3x " "=5 + y#

But #3x" is the same as "3x#!!

Therefore #" " 7 - y = 5 + y#
solve for y: #" " 7-5 = 2y#
#" " 2 = 2y " " rArr y = 1#

If #y = 1#, substitute into either equation to find #x#.

#3x = 7 - y rArr 3x = 7-1 = 6#
#3x = 6#
#x = 2#