How do you solve the system of equations #6x-5y=5# and #3x+5y=4#?

1 Answer
EZ as pi
Jul 2, 2016

#x = 1 and y = 1/5#

Explanation:

This is the perfect type of example for solving simultaneous equations by the elimination method, because the two y-terms are additive inverses and add to give 0.

#" " 6x color(red)(- 5y) =5 " ..................A"#
#" " 3x color(red)(+ 5y) =4 " ..................B"#
#"A+B " 9x " " =9 " ..................C"#
#" " x " " = 1#

Subs #1# for #x# in B:# " " 3(1) + 5y =4 #

#3+ 5y = 4 rArr 5y = 1 rArr y = 1/5#

It seems that #x=1 and y = 1/5#
Subs into A to check:

#6(1) - 5(1/5) = 6 -1 = 5#

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