Question

Parallel, perpendicular, or neither? 5x+3y=7 3x+5y=4

Answer 1

`k:y=m_1x+b_1;\ l:y=m_2x+b_2\\\\k\ \perp\ l\iff m_1\cdot m_2=-1\\\\k\ ||\ l\iff m_1=m_2`

`k:5x+3y=7\ \ \ |-5x\\\\3y=-5x+7\ \ \ \ |:3\\\\y=-(5)/(3)x+(7)/(3)\to m_1=-(5)/(3)\\\\l:3x+5y=4\ \ \ \ |-3x\\\\5y=-3x+4\ \ \ \ |:5\\\\y=-(3)/(5)+(4)/(5)\to m_2=-(3)/(5)`

`m_1\\eq m_2\to\text{ not parallel}\\\\m_1\cdot m_2=\left(-(5)/(3)\right)\cdot\left(-(3)/(5)\right)=1\\eq-1\to\text{ no perpendicular}`

Answer: NEITHER

Answer 2

Neither. They can’t be parallel because both lines have different slopes. They aren’t perpendicular either because their slopes don’t multiply to equal -1.