Simultaneous Equations. 3x-y=23, 2x+3y=8 What is x and y?

3x - y = 23         (1)

2x + 3y = 8        (2)

Multiply all terms in (1) by 3 

9x - 3y = 69      (3)

Now there are the same number of y's in equation (3) as in equation (2), so add equation (2) to equation (3) term by term:

11 x = 77

so x = 11

Plug this back into equation (1)

3*11 - y = 23  or 33 - y = 23

Subtract 23 from both sides

10 - y = 0

Add y to both sides

10 = y   (or y = 10)

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That is a great explanation - thanks Alan :)