Question

3x - 4y = 19; 8x + y = 12 Are the equations parallel, perpendicular, or neither

Answer 1

Step-by-step explanation:

Hey, there!

Let's check whether the lines are parallel, perpendicular or neither.

Fistly let's check of parallel ,

Let me tell you when two st. lines are paralle, then their slope are equal.

Given equation are,

3x - 4y = 9.........(i)

8x+y = 12 ..........(ii)

Now,

From equation (i)

$slope \: (m1) = \frac{ - coffe. \: ofx}{coffe. \: of \: y}$

$\: slope \: (m1) = \frac{ - 3}{ - 4}$

$therefore \: slope \: (m1) = \frac{3}{4}$

now, again slope from equation (ii).

$slope(m2) = \frac{ - coffe.of \: x}{coffe. \: of \: y}$

$slope \: (m2) = \frac{ - 8}{1}$

Therefore, the slope of equation (ii) is -8.

Since, Their slopes are not equal, they are not parallel.

Now, let's check for perpendicular,

To be perpendicular, slope (m1)× slope (m2)= -1

now,

$= \frac{3}{4} \times - 8$

= 3×-2

= -6.

So, the equations are neither parallel nor perpendicular.

Hope it helps...