SOLUTION: Please help me solve this linear system equation: x+y=10 2x=y-13 Need to find x and y also could you please give step by step how you solved the equation... Thank you!

Algebra ->  Coordinate Systems and Linear Equations -> SOLUTION: Please help me solve this linear system equation: x+y=10 2x=y-13 Need to find x and y also could you please give step by step how you solved the equation... Thank you!      Log On


   

Question 253260: Please help me solve this linear system equation:
x+y=10
2x=y-13
Need to find x and y
also could you please give step by step how you solved the equation...
Thank you!
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
x%2By=10 Start with the first equation.


2%28x%2By%29=2%2810%29 Multiply both sides by 2.


2x%2B2y=2%2810%29 Distribute


2x%2B2y=20 Multiply


highlight%28y-13%29%2B2y=20 Plug in 2x=y-13. In other words, replace each '2x' with 'y-13' (that's why I multiplied both sides by 2 above).


3y-13=20 Combine like terms on the left side.


3y=20%2B13 Add 13 to both sides.


3y=33 Combine like terms on the right side.


y=%2833%29%2F%283%29 Divide both sides by 3 to isolate y.


y=11 Reduce.


2x=y-13 Move onto the second equation


2x=11-13 Plug in y=11


2x=-2 Subtract


x=%28-2%29%2F%282%29 Divide both sides by 2 to isolate x.


x=-1 Reduce.

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Answer:


So the solutions are x=-1 and y=11 giving us the ordered pair (-1,11).