1st question
Solve the following pair of equations:
9a + 2 b = 54
a + 2 b = 6
2nd question
Solve:
10 a + 3 b = 12
3 a + 5 b = 20
3rd question
Solve the following equations:
5 v + 3 w = 11
4 v + 6 w = 16
Answers
Answer:
Q1. a = 6 b = 0.5
Q2. a = -10 b = 4
Q3. v =1 w = 2
Step-by-step explanation:
Sol1.
Eliminating the equations
9a + 2b = 54
a + 2b = 6
(-) (-) (-)
__________
8a = 48
a = 48/8
a = 6
Substituting value of a in eq 2
a + 2b = 6
6 + 2b = 6
2b = 6-6
b = 1/2
b = 0.5
Sol2.
(10a + 3b = 12) × 3
(3a + 5b = 20) × 10
Eliminating the equations
30a + 9b = 36
30a + 50b = 200
(-) (-) (-)
_____________
- 41 b = - 164
Cancelling the minus signs
41 b = 164
b = 164/41
b = 4
Substituting value of b in eq 1
10a + 3b = 12
10a + 3(4) = 12
10a + 12 = 12
10a = 12-12
a = -10
Sol3.
(5v + 3w = 11) × 2
(4v + 6w = 16) × 1
Elimimating the equations
10v + 6w = 22
4v + 6w = 16
(-) (-) (-)
_____________
6v = 6
v = 6 - 6
v = 1
Substituting value of v in eq2
4v + 6w = 16
4(1) + 6w = 16
6w = 16 - 4
w = 12/6
w = 2