using elimination
The elimination method requires the coefficient (number multiplied by the variable) to be the same for one variable in both equations. Here, the invisible 1 in front of the a allows us to use elimination. When the signs are the same, we subtract; when different, we add. The 1a is positive in both equations, so we can subtract one entire equation from another to ELIMINATE the variable a.
a + 7b = 13

a + 4b = 4 < Make sure you subtract each of the terms in the second equation from the first.
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3b = 9 < the a's canceled, 7b  4b = 3b and 13  4 = 9
Now, we solve by dividing both sides of the equation by 3.
3b = 9
3 3
b = 3
So, we know b = 3 and to solve for a, we substitute b back into EITHER equation to solve for a.
a + 7b = 13
a + 7(3) = 13
a + 21 = 13
 21 21
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a = 8
So our solution, (a,b) can be written as (8, 3).