Given d1|| d2, calculate t? d1: x+y-1=0 d2:3x-ty-2=0

Expert Answers
hala718 eNotes educator| Certified Educator

d1: x+y -1= 0

==> y= -x +1 ....(1)

d2: 3x -ty -2 =0

==> y= (3/t)x -2/t

Since d1 and d2 are parallel, then the slop of d1 (m1) = the slope of d2 (m2)

m1= -1

m2 = 3/t

But m1= m2

==> -1 = 3/t

==> t= -3

Then:

d1: x + y -1 =0

d2: 3x +3y -2 =0

neela | Student

The a1x+b1y+c1 =0 and a2x+b2y+c2 = 0 are || if,

a1/a2 = b1/b2

Here  the || lines are x+y-1=0 and 3x-ty-2 = 0.

a1 = 1, b1 =1 .  a2 = 3 and b2 = -t. Therefore,

1/3  = 1/(-t) . Multiply by 3t.

t = -3

giorgiana1976 | Student

If the 2 given lines are parallel, then the values of their slopes are equal.

The given equations are  x+y-1=0 and 3x-ty-2=0, so we'll have to put them in the standard from, which is y = mx+n.

We'll start with x+y-1=0.

We'll isolate y to the left side:

y = -x+1

So, the slope can be easily determined as m1 = -1.

That means that the second slope has the same value, m2 = -1.

We'll put the other equation into the standard form, isolating y to the left side:

3x-ty-2=0

-ty = -3x + 2

We'll divide by -t:

y = 3x/t - 2/t

The slope m2 = 3/t

But m2 = -1, so 3/t = -1

t = -3

The line d2 is: 3x+3y-2=0

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