SOLUTION: I am trying to help my son but he left the textbook at school. If you can walk me through one example I should be able to do the rest. Solve each system using substitution: 5x

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Question 719414: I am trying to help my son but he left the textbook at school. If you can walk me through one example I should be able to do the rest.
Solve each system using substitution:
5x-6y=19
4x+3y=10
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
That system does not make substitution easy. I would solve it by a different method, but if those were the instructions, we'll have to do substitution.

The traditional way:
STEP 1
Solve one of the equations for one of the variables.
(If one of the variables had a coefficient of 1 or -1, that would be the variable I would solve for. In this case, I do not see what the best choice is).
5x-6y=19 --> 5x-6y%2B6y=19%2B6y --> 5x=6y%2B19 --> 5x%2F5=%286y%2B19%29%2F5 --> x=%286%2F5%29y%2B19%2F5

STEP 2
In the other equation, substitute the expression found for the variable.
4x%2B3y=10 --> 4%28%286%2F5%29x%2B19%2F5%29%2B3y=10 --> %284%2A6%2F5%29y%2B4%2A19%2F5%2B3y=10 --> %2824%2F5%29y%2B76%2F5%2B3y=10
At this point, I would multiply both sides of the equal sign times 5 to get rid of denominators and I would get
24y%2B76%2B15y=50 --> 39y%2B76=50 --> 39y=50-76 --> 39y=-26 --> y=-26%2F39 --> highlight%28y=-2%2F3%29

STEP 3
Substitute the value found for the one variable to find the other variable.
4x%2B3y=10 --> 4x%2B3%28-2%2F3%29=10 --> 4x-2=10 --> 4x=12 --> highlight%28x=3%29

It seems like it would have been a little easier to solve for y in STEP 1.

A SMARTER WAY:
4x%2B3y=10 --> 3y=10-4x
Multiplying both sides of the equal sign times 2, we get
6y=20-8x
Substituting the expression found for 6y we get
5x-6y=19 --> 5x-%2820-8x%29=19 --> 5x-20%2B8x=19 --> 13x-20=19 --> 13x=19%2B20 --> 13x=39 --> x=39%2F13 --> highlight%28x=3%29
Substituting 3 for x in one of those equations, we get
4x%2B3y=10 --> 4%2A3%2B3y=10 --> 12%2B3y=10 --> 3y=10-12 --> 3y=-2 --> highlight%28y=-2%2F3%29