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

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) (Show Source): You can put this solution on YOUR website!

Start with the given system of equations:

Multiply the both sides of the second equation by 2.

Distribute and multiply.

So we have the new system of equations:

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

Group like terms.

Combine like terms. Notice how the y terms cancel out.

Simplify.

Divide both sides by to isolate .

Reduce.

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

Now go back to the first equation.

Plug in .

Multiply.

Subtract from both sides.

Combine like terms on the right side.

Divide both sides by to isolate .

Reduce.

So our answer is and .

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 (red) and (green)

Answer by Alan3354(69443) (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

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