Question

Find the number of solutions of the pair of linear equations x+2y-8=0 and 2x+4y=16

Answer 1

Step-by-step explanation:

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Answer 2

Given,

• x+2y-8=0 and 2x+4y=16 are given.

To find,

• We have to find a number of solutions to the pair of linear equations x+2y-8=0 and 2x+4y=16.

Solution,

We can simply find the number of solutions of the pair of linear equations x+2y-8=0 and 2x+4y-16=0 by using the following condition:

                      a1/a2 = b1/b2 = c1/c2               (*)

where a1 is the coefficient of x, b1 is the coefficient of y, and c1 is the constant in the first equation; a2 is the coefficient of x, b2 is the coefficient of y, and c2 is the constant in the second equation.

x+2y-8=0          (1)

2x+4y-16=0      (2)

a1 = 1, b1 = 2, c1 = -8; a2 = 2, b2 = 4, c2 = -16

Using (*), we get

                 1/2 = 2/4 = -8/-16

                 1/2 = 1/2   = 1/2

So, the number of solutions of the pair of linear equations x+2y-8=0 and 2x+4y=16 are infinitely many solutions.

Hence,  the number of solutions of the pair of linear equations x+2y-8=0 and 2x+4y=16 are infinitely many solutions.