My teacher didn't fully explain how to do this simultaneous equation?

Question

3a-19=5b (1)
6b-3a=-21 (2)

Answer 1

Add:-
6b - 19 = 5b - 21
6b - 5b = - 21 + 19
b = - 2

Answer 2

When solving simultaneous equations, you have to solve one of them to a point where you have just the "a" or the "b" on one side of the equation, then you insert that information into you second equation.

In this case, it looks like it will be easier to solve equation #2 first:

6b - 3a = -21
-3a = -21 - 6b (move 6b to the other side)
a = 7 + 2b (divide everything by -3)

So no you know that a is equal to (7 + 2b). Now just plug that information into equation #1.

3a - 19 = 5b
3(7 + 2b) = 5b (replace a with (7 + 2b))
21 + 6b -19 = 5b (multiply the 3 into the (7+2b))
2 = 5b - 6b (move the 6b to the other side)
2 = -b (5b - 6b equals -1b)
-2 = b

Now that you know b=-2, you have to figure out what a is. You can pick either equation, input b, and then solve for a.

3a - 19 = 5 * (-2) (input b = -2)
3a - 19 = -10 (multiply 5 * -2)
3a = 9 (bring -19 to the other side)
a = 3 (9 / 3 = 3)

Answer 3

3a - 19 = 5b
6b - 3a = -21
First bring the variables to one side and known values to the other side

3a - 19 = 5b take 19 to the other side ,the sign changes from negative to positive

3a = 5b + 19 take 5b to the other side , the sign changes from positive to negative
3a - 5b = 19 (3)

6b -3a = -21 just put -3a first we get

-3a + 6b = -21 (4) - no changes

add (3) and (4)

3a - 5b = 19
-3a+6b = -21
-------------------
0 + b = -2 or b = -2
3a and -3a cancel each other , 6b - 5b = b and 19 - 21 = -3

substitute b = -2 in either (1) , (2) , (3) or (4)

we will substitute b = -2 in (1)

3a - 19 = 5(-2)
3a - 19 = -10 take -19 to the other side ,sign changes

3a = -10+19 = 9
3a = 9
a = 9/3 = 3

You can substitue a = 3 and b = -2 in any of the equations to check if it gives the correct answer

3a - 5b = 19 (3)
3(3) - 5(-2) = 19
9+10 = 19 (two negatives make a positive)
19 = 19

6b - 3a = -21 (4)
6(-2) - 3(3) = -21
-12 -9 = -21
-21 = -21

Hope that clears all your doubts ;)

Answer 4

Rearrange (2)

-3a = -21-6b

Divide through by -3 to simplify

a = 7+2b

Now in equation (1) replace a with 7+2b

3(7+2b) - 19 =5b
21+6b-19=5b
2=5b-6b
2=-b
b= -2

Now sub this back into (2)

6(-2) - 3a = -21
-12 - 3a = -21
3a = 9
a = 3

Answer 5

3a-19=5b
6b-3a=-21
Rearrange the equations so that in both of the equations the a's and b's are in the same spot.
-3a-5b=19
-3a+6b= -21
Add these two equations together.
b= -2
Now that we know b, we should plug in this value into equation 1 to solve for a.
3a-19=5(-2)
3a-19= -10
3a=9
a=3
The problem is now complete now that we know both a and b.

Answer 6

3a-5b=19 (transposition)
-3a+6b=-21 (arranging) or this could also be 3a-6b=21

3a-5b=19 - 3a-6b=21

the result is b=-2 and a=3

*im not so sure about this, sorry