Question

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

Answer 1

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

Step-by-step 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).

Answer 2

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