7x-2y=17
2x+7y=73
solve by elimination

In order to solve by elimination we first need to find a common multiple of the x or y values. Lets eliminate x. 7 and 2 (both the x values) can both go into 14 without having any left over. In order to turn 7 into 14 we must multiply it by 2. But in this case, we'll multiply the entire equation by 2 in order to not change its value.
14x-4y=34
Now lets do the same for the second equation. In order to turn 2 into 14, we can multiply it by 7, but again we need to multiply the entire equation by 7 so we dont change it's value.
14x+49y=511

Now that we have the same coefficient on both the x's we can get rid of them by subtracting the two equations.

14x+49y=511
14x-4y=34

53y=477
y=9

Now that we have the value for y we can plug it in and solve for x.
7x-2(9)=17
7x-18=17
7x=35
x=5

The value of y is 9 and the value of x is 5.

7x - 2y = 17  (i)
2x + 7y = 73(ii)

Let us eliminate x,  multiply equation (i) by 2 and (ii) by 7.

7x - 2y = 17  (i)    x2
2x + 7y = 73(ii)    x7

2(7x - 2y) = 2(17)
14x - 4y = 34(iii)
7(2x + 7y) = 7(73)
14x + 49y =  511 (iv)

14x - 4y = 34(iii)
14x + 49y =  511 (iv)

We can now eliminate x by (iii) - (iv)
(14x - 4y) - (14x + 49y) = 34 - 511
14x - 4y -14x - 49y  = -477
14x - 14x - 4y - 49y = -477
0x -53y = -477
- 53y = - 477.
y = - 477/-53.   Use your calculator.
y = 9.

Now we can now substitute y = 9 in equation (i)   
7x - 2y = 17,  Recall y = 9
7x - 2(9) = 17
7x - 18 = 17
7x  = 17 + 18
7x = 35
x = 35/7 = 5.

Therefore, x = 5, y = 9.  Chrrs!