SOLUTION: Problem # 70 x + 3y = 2 -x + y = 1 Problem # 36 y = -3x + 19 y = 2x - 1 Problem # 24 4x + 5y = -2 4y - x = 11

Algebra ->  Coordinate Systems and Linear Equations  -> Lessons -> SOLUTION: Problem # 70 x + 3y = 2 -x + y = 1 Problem # 36 y = -3x + 19 y = 2x - 1 Problem # 24 4x + 5y = -2 4y - x = 11      Log On


   

Question 206456This question is from textbook Elementary and Intermediate Algebra
: Problem # 70
x + 3y = 2
-x + y = 1
Problem # 36
y = -3x + 19
y = 2x - 1
Problem # 24
4x + 5y = -2
4y - x = 11 This question is from textbook Elementary and Intermediate Algebra

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
I'll do the first one to get you started.



Start with the given system of equations:
system%28x%2B3y=2%2C-x%2By=1%29


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%28-1x%2By%29=%282%29%2B%281%29


%281x%2B-1x%29%2B%283y%2B1y%29=2%2B1 Group like terms.


0x%2B4y=3 Combine like terms.


4y=3 Simplify.


y=%283%29%2F%284%29 Divide both sides by 4 to isolate y.


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


x%2B3%283%2F4%29=2 Plug in y=3%2F4.


x%2B9%2F4=2 Multiply.


4%28x%2B9%2Fcross%284%29%29=4%282%29 Multiply both sides by the LCD 4 to clear any fractions.


4x%2B9=8 Distribute and multiply.


4x=8-9 Subtract 9 from both sides.


4x=-1 Combine like terms on the right side.


x=%28-1%29%2F%284%29 Divide both sides by 4 to isolate x.


So the solutions are x=-1%2F4 and y=3%2F4.


Which form the ordered pair .


This means that the system is consistent and independent.