Question

Given: 3j+k/2=15-4k; Prove j=10-3k


And Given 5x-2y=x+14; Prove y=2x-7

Answer 1

`j=10-3k`

`y = 2x - 7`

Explanation:

Solving (a):

Given

`(3j + k)/(2)=15-4k`

Required: Prove
`j=10-3k`

`(3j + k)/(2)=15-4k`

Multiply through by 2

`2 * (3j + k)/(2)=(15-4k) * 2`

`3j + k = 30 - 8k`

Subtract k from both sides

`3j = 30 - 9k`

Divide through by 3

`j = (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

`(-2y)/(-2) = (-4x)/(-2) + (14)/(-2)`

`y = 2x - 7`