Question

Pair of linear equations 3x+4y= 11 and 6x+8y= 22 is
intersecting, parallel and coincident?​

Answer 1

Concept Understanding :-

The linear equations is a equation which having highest power of degree 1

The equation can be expressed as ,

ax + by + c = 0

For finding lines

Compare the equation with a1x+b1y + c1 and

a2x +b2y + c2 = 0

a1/a2 ≠ b1/b2 forms intersecting lines it means they are having unique solution

a1/a2 = b1/b2 = c1/c2 forms coincident lines it means they are having infinite solution

a1/a2 = b1/b2 ≠ c1/c2 forms parallel lines it means they are having no solution.

Solution :-

Given equation

3x + 4y = 11 , 3x + 4y - 11 = 0

6x + 8y = 22 , 6x + 8y -22 = 0

Comparing the given equation with

a1x + b1y + c1 =0 and a2x + b2x + c2 = 0

Therefore ,

a1 = 3 , b1 = 4 , c1 = -11

a2 = 6 , b2 = 8 , c2 = -22

Now,

3/6 = 4/ 8 = -11/-22

1/2 = 1/2 = 1/2

Hence, It forms parallel lines $.$

Answer 2

$\huge \underline \mathfrak \purple{❁ Concept \: Understanding}$

The linear equations is a equation which having highest power of degree 1

The equation can be expressed as ,

ax + by + c = 0

For finding lines

Compare the equation with a1x+b1y + c1 and

a2x +b2y + c2 = 0

a1/a2 ≠ b1/b2 forms intersecting lines it means they are having unique solution

a1/a2 = b1/b2 = c1/c2 forms coincident lines it means they are having infinite solution

a1/a2 = b1/b2 ≠ c1/c2 forms parallel lines it means they are having no solution.

$\huge \underline \mathfrak \red{Solution}$

Given equation

3x + 4y = 11 , 3x + 4y - 11 = 0

6x + 8y = 22 , 6x + 8y -22 = 0

Comparing the given equation with

a1x + b1y + c1 =0 and a2x + b2x + c2 = 0

Therefore ,

a1 = 3 , b1 = 4 , c1 = -11

a2 = 6 , b2 = 8 , c2 = -22

Now,

3/6 = 4/ 8 = -11/-22

1/2 = 1/2 = 1/2

Hence, It forms parallel lines