Question

**Solve these systems of equations using addition to eliminate one of the variables.

14) 13a - b = 3
a + 3b = 11

21) a + 3b = 4
2a - b = 1

Answer 1

we can multiply any equation by any value; and also subtract the equations (or add) them together.

elimination is the process of multiplying the equations by a convient amount to get a variable that can be zeroed out

Answer 2

once a variable is eliminated, the problem is resolved by solving for the remaing variable

Answer 3

For question 14, I had gotten...

4a + 2b = 14

Now should I divide both side by 2 and solve from there?

Answer 4

the problem there is you still have 2 variables so we havent made the problem easier.

13a - b = 3
a + 3b = 11
^^
notice the bs here, if we multiply the top by 3 we can cancel these out



39a - 3b = 9
a + 3b = 11
-------------
40a = 20

now its a cinch to solve for "a"

Answer 5

we can just as easily multiply the bottom one by -13 to eliminate the "a" s and solve for b

Answer 6

21 works in the same manner, but nicer since its got smaller values to play with

Answer 7

But can I still divide both side by 2 and solve from there?

Answer 8

lets try it for your idea and see if we can work it out

4a + 2b = 14 ; divide by 2

2a +b = 7 ; we still have no way of singling out a variable

Answer 9

you might be able to substitute it into one of the others, but that kinda defeats the purpose of doing it this way to begin with :)

Answer 10

But the direction state.. **Solve these systems of equations using 'addition' to eliminate one of the variables.

Answer 11

right, and when you "added" you did not "eliminate" a variable

Answer 12

first you multiply by a useful value to change the form of the eqautions into something that will eliminate when adding