Question

Given: 3j+k/2=15-4k; Prove j=10-3k And Given 5x-2y=x+14; Prove y=2x-7

Answer 1

Answer:

$j=10-3k$

$y = 2x - 7$

Step-by-step explanation:

Solving (a):

Given

$\frac{3j + k}{2}=15-4k$

Required: Prove $j=10-3k$

$\frac{3j + k}{2}=15-4k$

Multiply through by 2

$2 * \frac{3j + k}{2}=(15-4k) * 2$

$3j + k = 30 - 8k$

Subtract k from both sides

$3j = 30 - 9k$

Divide through by 3

$j = \frac{30 - 9k}{3}$

j = 10 - 3k

Solving (b):

Given

$5x - 2y = x+ 14$

Required

Prove: $y = 2x - 7$

$5x - 2y = x+ 14$

Subtract 5x from both sides

$-2y = x - 5x + 14$

$-2y = -4x + 14$

Divide through by -2

$\frac{-2y}{-2} = \frac{-4x}{-2} + \frac{14}{-2}$

$y = 2x - 7$