SOLUTION: what is the value of x and y and what are the steps taken??? x+3y=23 -x+4y=12

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Question 580217: what is the value of x and y and what are the steps taken???
x+3y=23
-x+4y=12
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=23%2C-x%2B4y=12%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-x%2B4y%29=%2823%29%2B%2812%29


%28x-x%29%2B%283y%2B4y%29=23%2B12 Group like terms.


0x%2B7y=35 Combine like terms.


7y=35 Simplify.


y=%2835%29%2F%287%29 Divide both sides by 7 to isolate y.


y=5 Reduce.


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x%2B3y=23 Now go back to the first equation.


x%2B3%285%29=23 Plug in y=5.


x%2B15=23 Multiply.


x=23-15 Subtract 15 from both sides.


x=8 Combine like terms on the right side.


So the solutions are x=8 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=23 (red) and -x%2B4y=12 (green)