Question

PLEASE ANSWERRR! FIRST CORRECT ANSWER WILL VOTE BRAINLIEST

Answer 1

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