using elimination
what is the answer to a+7b=13 and a+4b=4
2 Answers
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.
______________
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
___________
a = 8
So our solution, (a,b) can be written as (8, 3).
a + 7b = 13
–
a + 4b = 4
0 + 3b = 9
3b = 9 > b = 3
In second equation, let's substitute "b" by its value
a + 4 • 3 = 4
a = 4  12 > a =  8
The solution (a, b) of a system of two linear equations is ( 8, 3)

Check the answer
1.  8 + 7 · 3 = 13
13 = 13
2.  8 + 4 · 3 = 4
4 = 4