Question

1. What is the solution to the system of equations?

Answer 1

ANSWER

1a)

The given system of equation is:

$3x - 6y = - 12...(1)$
and

$x - 2y = - 8...(2)$
We make x the subject in equation (2) to get;

$x = 2y - 8...(3)$

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



$3(2y - 8) - 6y = - 12$




We expand the bracket to get,

$6y - 24 - 6y = - 12$


$6y - 6y = 24 - 12$


This implies that,

$0 = 12$

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
$3x - 6y = - 12$



Thus implies that,

$- 6y = - 3x- 12$


$y = \frac{1}{2} x + 2$


For the second equation, we have:



$- 2y = - x - 8$


$y = \frac{1}{2} x + 8$


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.