SOLUTION: Thanks in advance for anyone who can help me!! :) Solve using the addition method: x+3y=19 x-y= -1 Here's what I've done so far, I can't seem to get past it x+3y=19 x-y=

Algebra ->  Test -> SOLUTION: Thanks in advance for anyone who can help me!! :) Solve using the addition method: x+3y=19 x-y= -1 Here's what I've done so far, I can't seem to get past it x+3y=19 x-y=       Log On


   

Question 182817This question is from textbook Prentice Hall Algebra 1
: Thanks in advance for anyone who can help me!! :)
Solve using the addition method:
x+3y=19
x-y= -1
Here's what I've done so far, I can't seem to get past it
x+3y=19
x-y= -1
and I added them so I have this: 2x+2y=18. I'm not even sure if that's right.
 This question is from textbook Prentice Hall Algebra 1

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

Start with the given system of equations:
system%28x%2B3y=19%2Cx-y=-1%29


3%28x-y%29=3%28-1%29 Multiply the both sides of the second equation by 3. The goal here is to get the "y" coefficients equal but opposite.


3x-3y=-3 Distribute and multiply.


So we have the new system of equations:
system%28x%2B3y=19%2C3x-3y=-3%29


Now add the equations together. You can do this by simply adding the two left sides and the two right sides separately like this:


%28x%2B3y%29%2B%283x-3y%29=%2819%29%2B%28-3%29


%28x%2B3x%29%2B%283y%2B-3y%29=19%2B-3 Group like terms.


4x%2B0y=16 Combine like terms.


4x=16 Simplify.


x=%2816%29%2F%284%29 Divide both sides by 4 to isolate x.


x=4 Reduce.


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x%2B3y=19 Now go back to the first equation.


4%2B3y=19 Plug in x=4.


4%2B3y=19 Multiply.


3y=19-4 Subtract 4 from both sides.


3y=15 Combine like terms on the right side.


y=%2815%29%2F%283%29 Divide both sides by 3 to isolate y.


y=5 Reduce.


So our answer is x=4 and y=5.


Which form the ordered pair .


This means that the system is consistent and independent.


Notice when we graph the equations, we see that they intersect at . So this visually verifies our answer.


Graph of x%2B3y=19 (red) and x-y=-1 (green)