Question

solve the following simultaneous equation : 20u - 30v = 13, 10v - 10u = -5​

Answer 1

Answer:

u = 0.2, v = -0.3

Step-by-step explanation:

Equation (1): 20u - 30v = 13

Equation (2): 10v - 10u = -5

Equation (2) x 2 : 20v - 20u = -10

Equation (1) + Equation (2):

(20u - 30v) + (20v - 20u) = 13 + (-10)

20u - 30v + 20v - 20u = 3

-10v = 3

v = -0.3

Sub v = - 0.3 into (1):

20u - 30(-0.3) = 13

20u + 9 = 13

20u = 4

u = 0.2

Answer: u = 0.2, v = -0.3

Answer 2

$20u - 30v \: = 13 \: \: ... equation \: (1) \\ \\ - 10u + 10v = - 5...equation \: (2) \\ \\ take \: equation(1) \: + 2 \times equation(2) \\ \\ \: \: 20u - 30v = 13 \\ - 20u + 20v = - 10 \\ \\ \: - 10v = 3 \\ \\ = > \: \: v = - \frac{3}{10}.....ans \\ \\ value \: of \: \: v \: put \: in \: any \: equation \\ \\ \\ - 10u + 10( - \frac{3}{10} ) = - 5 \\ \\ \: \: - 10u - 3 = - 5 \\ \\ - 10u = - 5 + 3 \\ \\ \: - 10u = - 2 \\ \\ \: \: = > u = \frac{2}{10} \\ \\ = > u = \frac{1}{5} ....ans$