How do you solve the system of equations #3x - 9y = 9# and #2x - 6y = - 4#?
1 Answer
These lines are parallel and do not intersect. The solution is the empty set.
Explanation:
One way starts by finding a multiplier that when applied to one equation, will change the coefficient of
Here, if we multiply the second equation by 1.5, we get:
When we compare this to the first equation, we note that the left side is identical, which would imply that the right sides should be as well. But this says -6 = 9!
Clearly this is false, so the only conclusion is that the line do not have a point where they intersect. In other words, the solution set is empty,and the lines are parallel.
Another way to do this is do convert each equation into slope-intercept form:
If you do this, you will find that the first equation is
while the second equation is
Since the lines have the same slope, they are parallel. The
Parallel lines do not intersect, as previously shown.
