0 0

what is the answer to a+7b=13 and a+4b=4

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.
______________
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)
-----------