Question

|. On comparing the ratios , , and , find out whether lines representing following
pairs of linear equations intersect at a point, are parallel or coincident: 1) 3x+2y=5and2x–3y=7
2) 2x–3y=8and4x–6y=9
II. Which of following pairs of linear equations are consistent / inconsistent? 3) x+y=5,2x+2y=10
4) x–y=8,3x–3y=16
5) 2x+y–6=0,4x–2y–4=0

Answer 1

Answer:

(3) Given : 3 x + 2 y = 5 or 3 x + 2 y -5 = 0

and 2 x – 3 y = 7 or 2 x – 3 y -7 = 0

Comparing these equations with x + y + 1=0

And 2 x + 2 y + 2 = 0

We get,

1 = 3, 1 = 2, 1= -5  

2 = 2, 2 = −3, 2 = −7

1 /2 =  3 /2  ,  1 /2  =  2 /−3  ,   1/ 2  =  −5 /−7  =  5/ 7

Since, 1 /2  ≠  1 /2

So, the given equations intersect each other at one point and they have only one possible solution. The

equations are consistent.

(2) Given 2x – 3y = 8 and 4x – 6y = 9

Therefore,

1 = 2, 1 = −3, 1= -8

2 = 4, 2 = −6, 2 = −9

1 /2  =  2 /4  =  1/ 2  ,  1/ 2  =  3/ 6  =  1 /2  ,  1/ 2 = 8 /9

Since, 1 /2  =  1/ 2  ≠  1/ 2

So, the equations are parallel to each other and they have no possible solution. Hence, the equations are

inconsistent.

(3) Given, x + y = 5 and 2x + 2y = 10

1 /2 = 1/ 2 ,  1 /2 = 1/ 2 , 1/ 2 = 5 /10 = 1 /2

,

1 /2 = 1 /2 = 1 /2

∴ The equations are coincident and they have infinite number of possible solutions.

So, the equations are consistent.

For, x + y = 5 or x = 5 - y

x= 4         3          2

y=1           2          3

For 2x + 2y = 10 or x=10-2 y/2

x=4    3    2

y=1    2    3

 As, we can see, that the lines are overlapping each other.

Therefore, the equations have infinite possible solutions.

(4) Given, x – y = 8 and 3x – 3y = 16

1 /2 = 1 /3 , 1 /2 = −1 /−3 = 1 /3 , 1 /2 = 8 /16 = 1 /2

,

1 /2 = 1 /2 ≠ 1 /2

The equations are parallel to each other and have no solutions. Hence, the pair of linear equations is

inconsistent.

(5) Given, 2x + y – 6 = 0 and 4x – 2y – 4 = 0

1 /2 = 2 /4 = 1 /2 , 1 /2 = 1 /−2 , 1 /2 = −6 /−4 = 3 /2

,

1 /2 ≠ 1 /2

The given linear equations are intersecting each other at one point and have only one solution. Hence,

the pair of linear equations is consistent.

Now, for 2x + y – 6 = 0 or y = 6 - 2x

x=0     1     2

y=0    4     2

And for 4x – 2y – 4 = 0 or = 4x-4/2

x=1    2    3

y=0   2    4

it can be seen that these lines are intersecting each other at only one point,(2,2).

SORRY! AS THERE IS NO GRAPH BUT I HOPE YOU WILL MANAGE.

Answer 2

Answer:

thanks for free points