SOLUTION: decide whether the pair of lines is parallell, perpendiculr or neither:? 3x + 2y = 3 2x + 3y =8 solve the following syestem of equations x + 4y = 7 x = 2 -4y

Question 192610: decide whether the pair of lines is parallell, perpendiculr or neither:?
3x + 2y = 3
2x + 3y =8
solve the following syestem of equations
x + 4y = 7
x = 2 -4y
Answer by RAY100(1637) (Show Source): You can put this solution on YOUR website!
checking the slopes by using the slope intercept form, (y=mx+b), we define parallel if m1=m2, and perpendicular if m1=1/-m2.
3x+2y=3
subt 3x both sides
2y=-3x+3
divide by 2 both sides
y=(-3/2)x+(3/2), therefore slope if (-3/2)
2x+3y=8
subt 2x both sides
3y=-2x+8
divide both sides by 3
y=(-2/3)x +8, therefore slope is (-2/3)
comparing slopes 0f (-3/2) and (-2/3) they are neither parallel nor perpendicular
second problem
(1) x+4y=7
(2) x=2-4y
substitute (2) into (1)
(2-4y) +4y=7
2=7
therefore no solutions
restating (2) as x+4y=2
we can see that (1) & (2) are parallel with different y intercepts
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