ok i had a maths exam today and i couldnt work out this equation i spent like 20 mins on it can you help?

Question

it was

5a+3b=9 and 2a-3b=12

a=
b=

it has really been bugging me as i cn work them out a and b have to be the same in each equatuion

Answer 1

adding both 7a=21
dividing by 7
a=3
sub in (1)
15+3b=9
adding -15
3b=-6
dividing by 3
b=-2

Answer 2

These are simultaneous equations. They can be solved by two methods called SUBSTITUTION and ELIMINATION

Method 1: Substitution

5a + 3b = 9

3b = 9 - 5a

b = (9 -5a)/3

Substitute for b in the 2nd equation

2a - 3 (9 -5a)/3 = 12

2a - 9 + 5a = 12

7a = 12 + 9

a = 21/7

a = 3

To find b, substitute for a in one of the equations:

5 *3 + 3b = 9

3b = 9 -15

b = -6/3

b = -2

Check with the 2nd equation:

2*3 - 3*(-2) = 12

6 + 6 = 12 OK

Answer: a = 3 and b = -2

Method 2: Elimination

(1) 5a + 3b = 9
(2) 2a - 3b = 12

Add (1) to (2) gives:

(3) 7a = 21
a = 3

Substitute for a in (1) or (2) and check as per method 1

Sorry to hear you got stuck in the exam. It happends to evryone at some stage and you could kick yourself when you see what you should have done.

Answer 3

5a+3b=9
2a-3b=12

add lefts and rights
5a + 3b + 2a - 3b = 9 + 12
add same with same:
5a + 2a + 3b - 3b = 21
7a + 0 = 21
7a = 21 /:7 (divide both sides by 7)
a = 3

plug a into one of the equations, for example, 5a+3b=9
5a+3b=9
a = 3
------------
5*3 + 3b = 9
15 + 3b = 9 (transfer 15 to the right, and give it an opposite sign: 15 will turn into -15)
3b = 9 - 15
3b = -6 /:3 (divide both sides by 3, to solve for b)
b = -2

Check:
plug a i b into both equations:
5a+3b=9; a = 3, b = -2
5*3 + 3*(-2) = 9
15 - 6 = 9
9 = 9 OK!


2a-3b=12
2*3 -3*(-2) = 12
6 + 6 = 12
12=12 OK!

The equations are valid for a = 3, b = -2, which is the system solution.

Answer 4

5a + 3b = 9 and 2a - 3b = 12. Use a simultaneous equation where you have to add the 2 equations 2a - 3b + 5a + 3b = 12 - 9
Therefore 3b and -3b gets cancelled leaving us with 7a = 3.
Then 7a/7 = 3/7. a = 3/7. Then substitute the value of a in any one of the equations in this instance 2a - 3b = 12.
2*3/7 - 3b = 12. Then -3b = 12 - 6/7. -3b = 84/7 - 12/7.
Then -3b = 72/7, -3b/-3 = 72/7*1/3. b = 24/7.
So answer to your question is a = 3/7 and b = 24/7

Answer 5

simply add the two equations
then,
5a + 3b +2a -3b = 9 +12
the b terms cancel each other out, then,

7a = 21
dividing both sides by 7 gives a=3
substitute 3 instead of a in the 1st equation, then,

5(3) + 3b = 9
3b = 9 - 15
3b = -6
b = -2

Answer 6

The easiest way is to sum both equations, as follows:

5a + 3b = 9
2a - 3b = 12
----------------
7a + 0 = 21

so, a= 21 / 7; a = 3

Then get b from any of the original equations:

5a + 3b = 9

so, 3b = 9-5a ; b = (9-5a) / 3

replace a by its value: 3

b= (9 - 5(3)) / 3;
b=(9-15) / 3;
b= -6 / 3
b= -2

If you replace this values on the original equations, you will confirm they are correct!

Good luck!

Answer 7

Just add the equations (one to the other):
(5a + 3b = 9)
(2a - 3b = 12)
------------------
(7a + 0b = 21)

7a = 21 then a = 3

use first equation with a = 3:
5a + 3b = 15 + 3 b = 9
then 3 b = -6
b = -2

I remember having similar problems on exams: questions that are too easy to solve under pressure. That's OK, I survived.

Answer 8

Add both the equations
i.e., 5a+3b+2a-3b=9+12
= 7a=21
a=3

Put the value of "a" in any equation
5x3 + 3b = 9
3b = 9-15
3b = -6
b = -2

Answer 9

5a+3b = 9
2a-3b = 12

cancel the -3b and +3b

therefore
5a=9
2a=12

Add the 5a + 2a= 7a
Add 9 + 12 = 21

7a=21
a= 3

Sub a into equation to find b
5a+3b=9
5(3) +3b=9
15+3b=9
3b=9-15
3b= -4
b= -4/3, -1 1/3

a= 3
b = -1 1/3

I think

Answer 10

Lets solve for a in the first equation.

5a + 3b = 9
5a = 9 - 3b
a = (9 - 3b) / 5

Now, put that in for a in the second equation


2a - 3b = 12
2 ( (9 - 3b) / 5 ) - 3b = 12
If we multiply everything by 5 we can clear the fraction
2(9 - 3b) - 15b = 60
18 - 6b - 15b = 60
18 - 21b = 60
-21b = 42
b = -2

Now you can put b = -2 into either equation to find a. We will just use the first one again.

5a + 3b = 9
5a + 3(-2) = 9
5a - 6 = 9
5a = 15
a = 3

So your answer is a = 3 and b = -2

Answer 11

Line them up so that 5a is above 2a, then add the two equations together to get 7a=21. We divide both sides to get a=3. If 3 is substituted for a in either equation we get b= -2. I have made more mistakes that anyone assisting with this problem. I have learned greatly from those mistakes. Have a great day!!
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