Question

show that the lines are 3 X + 2 Y + 9 = 0 and 12 x + 8 Y - 15 = 0 are parallel lines

Answer 1

To show that they are parallel, I will put each of these equations into the form of $y=mx+b$

For the first equation, $3x+2y+9=0$ we begin by subtracting 3x and 9 from each side

This gives us $2y=-3x-9$

Next, we divide each side by 2.

This gives us the equation of $y=\frac{-3}{2}x-\frac{9}{2}$

Now we can solve the second equation, $12x+8y-15=0$

We can begin by subtracting 12x and adding 15 to each side

This gives us $8y=-12x+15$

Now we can divide each side by 8

This gives us $y=-\frac{12}{8}x+\frac{15}{8}$

This simplifies to $y= -\frac{3}{2}x+\frac{15}{8}$

As the slopes of each line are the same, $-\frac{3}{2}$, they are parallel to each other.

Answer 2

According to Pair of Linear equations in Two Variables ,

Two lines are parallel when they have no solution or when

a1/a2 = b1/b2 != c1/c2

Here equations are :

3x + 2y + 9 = 0 &

12x + 8y - 15 = 0


a1 = 3 , a2 = 12
b1 = 2 , b2 = 8
c1 = 9 , c2 = - 15

a1/a2 = 3/12 = 1/4
b1/b2 = 2/8 = 1/4
c1/c2 = 9/(-15) = -3/5

From above three equations we gets that

a1/a2 = b1/b2 != c1/c2

ie. 1/4 = 1/4 != -3/5

So this is a parallel line .





NOTE :- "!=" indicates "Not equal to"