Question

Solve the simultaneous equations:

3a-2b=14
4a+3b=13

Answer 1

a = 4 b = -1

Explanation:

13 = 4a - 3b (1)

14 = 3a + 2b (2)

(1) x 2

(2) x 3

26 = 8a - 6b (3)

42 = 9a + 6b (4)

(3) + (4)

68 = 17a

68/17 = 17a/17

a = 4

Substitute back in to original equation

14 = 3(4) - 2b

14 = 12 - 2b

14 - 12 = 12 -12 - 2b

2 = -2b

Divide by -2 both sides

b = -1

Check

3(4) - 2(-1)

12 + 2 = 14

Answer 2

Explanation:

3a-2b=14 multiply by 3

9a - 6b = 42 (1)

4a+3b=13 multiply by 2

8a +6b = 26 (2)

sum up (1) and (2)

17a = 68

a =4

b=-1