Question

Solve the system by substitution. x – 3y = 4 2x – 6y = 8

Answer 1

x-3y=4
2x-6y=8
=> -2x+6y=-8
2x-6y=8
=> 0=0

Answer 2

Answer: The given system of equations will have infinite number of solution.

Explanation: We are given to solve the following system of equations by substitution method :

`x-3y=4~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)\\\\2x-6y=8~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(ii)`

From equation (i), we have

`x-3y=4\\\\\Rightarrow x=4+3y~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(iii)`

Substituting the value of x from equation (iii) in equation (ii), we get

`2(4+3y)-6y=8\\\\\Rightarrow 8+6y-6y=8\\\\\Rightarrow 8=8,`

which is always true.

So, the given system of equations will have infinite number of solutions.

Let y = k, a real number. Then, from equation (iii), we get

`x=4+3k.`

Thus, all the solutions of the given system are given by

(x, y) = (4+3k, k).