Answer:
Step-by-step explanation:
Given system:
- x + y + 3z = 10,
- -4x + 3y + 5z = 7,
- kx + z = 3
Substitute z in the first two equations with z = 3 - kx:
- x + y + 3(3 - kx) = 10 ⇒ (1 - 3k)x + y = 1 ⇒ y = (3k - 1)x + 1
- -4x + 3y +5(3 - kx) = 7 ⇒ -(4 + 5k)x + 3y = -8 ⇒ y = 1/3(5k + 4) - 8
In order the two equations above not to have a solution, the lines should be parallel. Parallel lines have equal slopes.
Solve the following equation for k:
- 3k - 1 = 1/3(5k + 4)
- 9k - 3 = 5k + 4
- 4k = 7
- k = 7/4
