How do you solve the following linear system: #-x + 4y = -8 , 3x + 2y = 9 #?

1 Answer
mason m
Nov 14, 2015

Substitution.

Explanation:

Substitution Method
Solve for #x# in the equation #-x + 4y = -8#.

Subtract #4y# from both sides: #-x = -4y - 8#
Divide both sides by #-1#: #x = 4y + 8#
Now, knowing that #x = 4y + 8#, replace #x# in the other equation with #4y + 8#.

This gives: #3(4y + 8) + 2y = 9#
Distribute: #12y + 24 + 2y = 9#
Combine like terms on the left side: #14y + 24 = 9#
Subtract #24# from both sides: #14y = -15#
Divide both sides by #14#: #color(red)(y = -15/14)#

Now, plug in your new value for #y# in either equation.
Example: #3x + 2(-15/14) = 9#
Multiply: #3x + (-30/14) = 9#
Simplify: #3x - 15/7 = 9#
Add #15/7# to both sides and find a common denominator: #3x = 15/7 + 63/7#
Add: #3x = 78/7#
Divide both sides by #3#: #x = 78/15#
Simplify: #color(red)(x = 26/5)#

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