Question

15 points: can someone help me with this thank you. (all separate equations)

solve for y: 6x+3y=12

solve for k: 2p-k=3

solve for w: 6v-2w=10

Answer 1

Explanation:

`6x+3y=12\qquad\text{subtract}\ 6x\ \text{from both sides}\\\\6x-6x+3y=12-6x\\\\3y=12-6x\qquad\text{divide both sides by 3}\\\\(3y)/(3)=(12)/(3)-(6y)/(3)\\\\\large\boxed{y=4-2y}\\\\===================`

`2p-k=3\qquad\text{subtract}\ 2p\ \text{from both sides}\\\\2p-2p-k=3-2p\\\\-k=3-2p\qquad\text{change the signs}\\\\k=-3+2p\\\\\large\boxed{k=2p-3}\\\\===================`

`6v-2w=10\qquad\text{subtract}\ 6v\ \text{from both sides}\\\\6v-6v-2w=10\\\\-2w=10-6v\qquad\text{divide both sides by (-2)}\\\\(-2w)/(-2)=(10)/(-2)-(6v)/(-2)\\\\w=-5+3v\\\\\large\boxed{w=3v-5}\\\\===================`