SOLUTION: My worksheet says: Solve the system of equations: 3X+2Y=17 2X-Y=9 Please help thanks

Algebra ->  Systems-of-equations -> SOLUTION: My worksheet says: Solve the system of equations: 3X+2Y=17 2X-Y=9 Please help thanks      Log On


   

Question 161600: My worksheet says:
Solve the system of equations:
3X+2Y=17
2X-Y=9
Please help
thanks
Found 2 solutions by jim_thompson5910, Alan3354:
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%283x%2B2y=17%2C2x-y=9%29


2%282x-y%29=2%289%29 Multiply the both sides of the second equation by 2.


4x-2y=18 Distribute and multiply.


So we have the new system of equations:
system%283x%2B2y=17%2C4x-2y=18%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:


%283x%2B2y%29%2B%284x-2y%29=%2817%29%2B%2818%29


%283x%2B4x%29%2B%282y%2B-2y%29=17%2B18 Group like terms.


7x%2B0y=35 Combine like terms. Notice how the y terms cancel out.


7x=35 Simplify.


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


x=5 Reduce.


------------------------------------------------------------------


3x%2B2y=17 Now go back to the first equation.


3%285%29%2B2y=17 Plug in x=5.


15%2B2y=17 Multiply.


2y=17-15 Subtract 15 from both sides.


2y=2 Combine like terms on the right side.


y=%282%29%2F%282%29 Divide both sides by 2 to isolate y.


y=1 Reduce.


So our answer is x=5 and y=1.


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 3x%2B2y=17 (red) and 2x-y=9 (green)

Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
Solve the system of equations:
3X+2Y=17 eqn 1
2X-Y=9 eqn 2
------------
2X-Y=9 eqn 2
-y = 9-2x
y = 2x-9
Sub for y into eqn 1
3x + 2(2x-9) = 17
3x + 4x -18 = 17
7x = 35
x = 5
-----------
y = 2x-9
y = 1