Question

Please help me to solve the system of equations by substitution method.​

Answer 1

k = 0, v = -1.

Explanation:

Consider the first equation:

3 - 5(0.2v - 2k) = 3(3k + 2) + 2v

3 - v + 10k = 9k + 6 + 2v

10k - 9k = 2v + v + 6 - 3

k = 3v + 3

Now substitute for k in the second equation:

4(3v + 3 - 3v) - (2(3v + 3) + v) = 11 - 2(2(3v + 3) + v)

12 - (6v + 6 + v) = 11 - 2(6v + 6 + v)

12 - 6v - 6 - v = 11 - 12v - 12 - 2v

12 - 7v - 6 = - 1 - 14v

7v = -1 - 12 + 6

7v = -7

v = -1.

Now substitute v = -1 into the first equation to find the value of k:

3 - 5(0.2(-1) - 2k) = 3(3k + 2) +2(-1)

3 - 5(-0.2 - 2k) = 9k + 6 - 2

3 + 1 + 10k = 9k + 4

10k - 9k = 4 - 4

k = 0.

Now check these reslts by plgging these into second eqation

Left side = 4(0 - 3(-1)) - (2(0) - 1) = 12 + 1 = 13

right side = 11 - 2(0 + -1)) = 11 + 2 = 13.

This confirms the reslts.