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

Question

asked Nov 9, 2018 188k views

2 Answers

Yossi Zloof · Answer 1 · 2018-11-13T21:17:46+0000

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).