Question

3. Find atleast three solutions for each of the following linear equations in two variables:
(i) 2x + 5y - 13 = 0
(ii) x-3/4 y = 6
3= (√2-1)x=y​

Answer 1

Given: Three equations (i) 2x + 5y - 13 = 0  (ii) x-3/4 y = 6 (iii) (√2-1)x = y​

To find: at least three solutions for each of the following linear equations

Solution:

• Now we have given three equations:

              (i) 2x + 5y - 13 = 0

              Put x = 0, we get:

              2(0) + 5y = 13

              y = 13/5

              Put x = 1, we get:

              2(1) + 5y = 13

              y = 11/5

              Put x = 1, we get:

              2(-1) + 5y = 13

              y = 15/5

• So the solutions are: (0,13/5) , (1,11/5) , (-1,15/5)

               (ii) x - 3/4 y = 6

              Put x = 0, we get:

              y = 6(-4/3) = -8

              Put x = 1, we get:

              1 - 3/4 y = 6

              y = 5(-4/3) = -20/3

              Put x = -1, we get:

              - 1 - 3/4 y = 6

              - 3/4 y = 7

              y = 7(-4/3) = -28/3

• So the solutions are: (0,-8) , (1,-20/3) , (-1,-28/3)

              (iii) (√2-1)x = y​

              Put x = 0, we get:

              y = 0

              Put x = 1, we get:

              (√2-1) = y

              Put x = -1, we get:

              -(√2-1) = y

              y = 1 - √2

• So the solutions are: (0,0) , (1,√2-1) , (-1,1 - √2)

Answer:

               So the solutions are:

               (i) 2x + 5y - 13 = 0     (0,13/5) , (1,11/5) , (-1,15/5)

               (ii) x-3/4 y = 6           (0,-8) , (1,-20/3) , (-1,-28/3)

               (iii) (√2-1)x = y​           (0,0) , (1,√2-1) , (-1,1 - √2)

Answer 2

Step-by-step explanation:

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