How do you solve the following system?: # 2x + y = -5, 3x - 5y = 2 #

1 Answer
Noah G
Jan 9, 2016

Solving using substitution

Explanation:

2x + y = -5
y = -5 - 2x
3x - 5(-5 - 2x) = 2
3x + 25 + 10x = 2
13x = 2 - 25
13x = -23
x = #-23/13#

Substitute #-23/13# for x.

2(#-23/13#) + y = -5
#-46/13# + y = -5
y = #-19/13#

The solution set is (#-23/13#, #-19/13#).

Below are a few exercises to practice yourself. At the end, I put a linear-quadratic system a for a little bit of a challenge should you want it... Be warned of more than one solution set in the linear-quadratic system. Feel free to ask for help with the linear-quadratic system.

a) 2x + 3y = 6
x - 5y = -11

b) 4x - 7y = -12
2x - 14y = 3

c) #x^2# + 12x = -y - 13
-2x - y = 4

Enjoy!

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