1. what is the solution to the system of equations? 3x - 6y = -12 x -2y = -8 (a) use the substitution method to justify that the given system of equations has no solution. show all work! (b) what do you know about the two lines in this system of equations?

ANSWER

1a)

The given system of equation is:


and


We make x the subject in equation (2) to get;



We put equation (3) into equation (1) to get;



We expand the bracket to get,





This implies that,



This statement is false.

Hence the system has no solution.

1b)

Let us write the two systems in the slope-intercept form;

For the first equation, we have


Thus implies that,





For the second equation, we have:





We can see that, the two equations are parallel since they have the same slope.

Also the two equations will never meet since they have different y-intercepts.

Hence the system has no solution.