Solve the following simultaneous equations?

Question

5a + 3b = 26
3a + 2b = 16

Answer 1

I thought I would show you how to do this instead of just giving you the answer.

Let's take the second equation, 3A + 2B = 16. If we subtract 3A from both sides we get 2B = 16 - 3A, or B = 8 - 3/2A.

Putting this back into the other equation, we get 5A + 3*(8 - 3/2A) = 26, or 5A + 24 - 9/2A = 26, or (10/2 - 9/2A) or 1/2A = 2, or A = 4.

If A = 4, B =2 in either equation by going back to check.

Answer 2

a = 4 b = 2

Answer 3

(eq 1) 5a + 3b = 26
(eq 2) 3a + 2b = 16

Step 1: In eq 1, express a in terms of b...

5a = 26 - 3b
a = (26 - 3b) / 5

Step 2: In eq 2, substitute a with equation in Step 1...

3[(26 - 3b)/5] + 2b = 16
(3/5)(26) - (3/5)(3b) + 2b = 16
15.6 - 1.8b + 2b = 16
15.6 - 0.2b = 16
15.6 - 16 = 0.2b
-0.4 = 0.2b
b = -0.4 / 0.2
b = -2

Step 3: Solve for a (in Step 1), given b...

a = [26 - 3(-2)] / 5
a = (26 + 6) / 5
a = 32 / 5
a = 6.4

Therefore:

a = 6.4
b = -2

Answer 4

a=4, b=2

Multiply the top equation by 2, and the bottom equation by 3, to get rid of the variable "b".

10a + 6b = 52
9a + 6b = 48

Now, subtract the lower eq from the upper...

1a = 4
a=4

Now substitute 4 for a in the first equation:

5(4) + 3b = 26
20 + 3b = 26
3b = 6
b=2

Answer 5

a=4
b=2