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Linear Equation Two Variable

In Linear Equation Two Variable , we have to find unknown values of given condition.

Level 1  

1. Find the value of 'a' so that the point (3,a) lies on the line represented   by  2x - 3y = 5.

Solution:-

              As the point (3, a) lies on the line 2x - 3y = 5 ,Then we can say that the give point is a solution of that line .

Hence substitute x = 3 and y = a .

                               2x - 3y = 5

                               2(3) - 3(a) = 5

                               6 - 3a = 5

                               3a = 1

                               a = 1/3 .

Therefore, a = 1/3.

2. Find the value of 'k' so that the lines 2x - 3y = 9 and kx - 9y = 18 will be parallel.


Solution:-

             If  \(a_{1}x + b_{1}y + c_1 = 0\) and \(a_{2}x + b_{2}y + c_2 = 0\) are parallel lines then,

                         \(\frac {a_1}{a_2} = \frac{b_1}{b_2} \neq \frac{c_1}{c_2}\)

           Hence, If 2x - 3y = 9 and kx - 9y = 18 are parallel lines then ,

                           \(\frac {2}{k} = \frac{-3}{-9} \neq \frac{9}{18}\)
                           \(\frac {2}{k} = \frac{3}{9}\)                                                

                            2*9 = 3*k                             

                            k = 6

Therefore, k = 6.

3. Find the value of 'k' for which x + 2y = 5 and 3x + ky + 15 = 0 is inconsistent.

Solution:-

             If  \(a_{1}x + b_{1}y + c_1 = 0\) and \(a_{2}x + b_{2}y + c_2 = 0\) are inconsistent then,

                         \(\frac {a_1}{a_2} = \frac{b_1}{b_2} \neq \frac{c_1}{c_2}\)

           Hence, If x + 2y = 5 and 3x + ky = -15 are inconsistent then ,

                           \(\frac {1}{3} = \frac{2}{k} \neq \frac{5}{-15}\)

                           \(\frac {1}{3} = \frac{2}{k}\)

                           1*k = 3*2

                           k = 6

Therefore, k = 6.


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