Question

Solve for the two unknowns. 3a + 4b = 12 2a + 2b = 15

Answer 1

2a+2b=15
⇒ 2(2a+2b)= 2*15
⇒ 4a+ 4b= 30 (1)

3a+4b= 12 (2)

Take (1)-(2), we have:
(4a-3a)+ (4b-4b)= 30-12
⇒ a= 18

2b= 15- 2a
⇒ 2b= 15-2*18
⇒ 2b= 15- 36
⇒ 2b= -21
⇒ b= -21/2

Final answer: a= 18, b= -21/2~

Answer 2

Let us take the second equation first for finding the value of a
2a + 2b = 15
2a = 15- 2b
a = (15/2) - b
Now let us put the value of a found from the second equation in the first equation. We get
3a + 4b = 12
3[(15/2) - b] + 4b = 12
45/2 - 3b + 4b = 12
b = 12 - (45/2)
= (24 - 45)/2
= - 21/2
Now putting the value of b in the second equation, we get
2a + 2b = 15
2a + [2 * (- 21/2)] = 15
2a - 21 = 15
2a = 15 + 21
2a = 36
a = 36/2
= 18
So from the above solutions we come to know that the value of a is 18 and the value of b is - 21/2(minus twenty one divided by 2).