Question

check whether the pair of equations 3x-2y+2=0 , 3/2x-y+3=0 is consistent . also find the coordinates of the points where the graphs of the equations meet the y-axis.

Answer 1

Given : the pair of equations 3x-2y+2=0 and 3/2x-y+3=0

To find : check graphically whether  it  is consistent .

The coordinate of the points where the graphs of the equation meet the y axis

Solution:

pair of linear equation

Consistent       if  unique solution or infinite solution

pair of linear equation

Inconsistent   if  no solution  

a₁x  + b₁y   + c₁ = 0

a₂x  + b₂y  + c₂  = 0

if a₁ /a₂   ≠   b₁/b₂       Consistent & unique solution    (Intersecting lines)

a₁ /a₂   =   b₁/b₂    ≠   c₁/c₂   Inconsistent  having no solution ( Parallel lines )

a₁ /a₂   =   b₁/b₂    =   c₁/c₂   Consistent  having infinite solution ( coinciding lines )

3x - 2y + 2 = 0

(3/2)x - y + 3 = 0

=> 3/(3/2)  = 2  

- 2/-1  = 2

2/3

2 = 2   ≠  2/3

Hence inconsistent

not consistent

Parallel  lines

From Graph also line s are parallel

3x - 2y + 2 = 0    meets  y axis at (0,1)

(3/2)x - y + 3 = 0 meets  y axis at (0,3)

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Answer 2

Answer:

Concept:  using consistency concept of linear equation .

Given: the pair of equations 3x-2y+2=0 , 3/2x-y+3=0 is consistent .the pair of equations 3x-2y+2=0 , 3/2x-y+3=0.

To find: the pair of equations 3x-2y+2=0 , 3/2x-y+3=0 is consistent .

Step-by-step explanation:

pair of linear equation

Consistent       if

unique solution or infinite solution

pair of linear equation

Inconsistent   if  no solution  

a₁x  + b₁y   + c₁ = 0

a₂x  + b₂y  + c₂  = 0

if a₁ /a₂   ≠   b₁/b₂       Consistent & unique solution    (Intersecting lines)

a₁ /a₂   =   b₁/b₂    ≠   c₁/c₂   Inconsistent  having no solution ( Parallel lines )

a₁ /a₂   =   b₁/b₂    =   c₁/c₂   Consistent  having infinite solution ( coinciding lines )

$3x - 2y + 2$ = 0

$(\frac{3}{2})x - y + 3$ = 0

=> $3/(\frac{3}{2})$ = $2$  

$- 2/-1$  = $2$

$\frac{2}{3}$

$2$ = $2$   ≠ $\frac{2}{3}$

Hence inconsistent

not consistent

Parallel  lines

From Graph also line s are parallel

$3x - 2y + 2$ = 0    meets  y axis at ($0,1$)

$(\frac{3}{2})x - y + 3$= 0 meets  y axis at ($0,3$)

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