This is a free lesson from our course in Algebra I
In this lesson, we'll explain how to find out whether a system of equations has
no solution. In a system of two linear equations Ax + By + C =
0 and Dx + Ey + F = 0, the only circumstance in which the system
of equation would have no solution is when the lines are parallel, i.e. they have
the same slope and they don't overlap. Then there can be no points that are common
to both lines. In case of this system of two linear equations, the two lines
are parallel if A/B = D/E. For example, 5x - 3y = 1 and 15x
- 9y = 5 have no solution because A/B = D/E = -5/3. (More text below video...)
(Continued from above) For example, Solve the system of linear equations. 4x - y = 8 -8x + 2y = -5 Steps to solve this example: • multiply all terms in the first equation by 2,
8x - 2y = 16 -8x + 2y = -5 • add the two equations 0x + 0y = 11 or 0 = 11
• conclusion: Because there are no values of x and y for which 0x + 0y = 11, the given system of equations has no solutions. This system is inconsistent.
Winpossible's online math courses and tutorials have gained rapidly popularity since
their launch in 2008. Over 100,000 students have benefited from Winpossible's courses...
these courses in conjunction with free unlimited homework help serve as a very effective
math-tutor for our students.
All of the Winpossible math tutorials have been designed by top-notch instructors
and offer a comprehensive and rigorous math review of that topic.
We guarantee that any student who studies with Winpossible, will get a firm grasp
of the associated problem-solving techniques. Each course has our instructors providing
step-by-step solutions to a wide variety of problems, completely demystifying the
Winpossible courses have been used by students for help with homework and by homeschoolers.
Several teachers use Winpossible courses at schools as a supplement for in-class
instruction. They also use our course structure to develop course worksheets.