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2 years ago

PLEASE ANSWERRR! FIRST CORRECT ANSWER WILL VOTE BRAINLIEST

Mathematics

1 answer:

FinnZ [79.3K]2 years ago

8 0

Answer:

k = 7/4

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

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