+1443 What would be the easiest way to solve these two problems, and how would I solve them using those ways? (these are practice problems and they are for getting answers and understanding how it's done. It isn't a test or anything like that.)
4x + 7y = 6
9x - 2y = 49
and
3x - y = 4
y = 2x - 2
+2863 When looking at systems of linear equations. You can either use substitution or elimination.
The question is WHICH one to use?
Don't skim my answer for the answer
(ax with a being the constant)
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Substitution. You should use this whenever you see a variable with a constant of 1. For example the second equation you posted.
3x - y = 4
y = 2x - 2
Notice how this can EASILY be substituted
Solving:
3x - (2x-2) = 4 (remember there is a -1 multiplying at the parentheses).
(remove parentheses and combine like terms.)
x + 2 = 4
x = 2
Now substitute back into one of your equations and find y.
Elimination. You should use this whenever you can't divide both sides of one of the equations and get integer constants.
4x + 7y = 6
9x - 2y = 49
Notice how the equation will be difficult substituting. If you try to isolate a variable, you will get fraction constants.
So a good strategy is to find the greatest common multiple.
Solving:
4x + 7y = 6 (Mulitply 7y by 2)
9x - 2y = 49 (Multiply 2y by 7)
8x + 14y = 12
63x - 14y = 343
Now you can just add both equations: 71x = 355
Then divide - x=5
Now substitute back into one of the equations and find y
