Solving Linear Systems of Equations by Elimination
Use elimination to find the solution of this system.
To make the equations easier to work with:
Both variables are eliminated. The result is the false statement 0 = 31.
|â€¢ Clear the fractions in the
first equation by multiplying
both sides by 6, the LCD of
|â€¢ Clear the decimals from
the second equation by
multiplying both sides
|| 10(0.3x + 0.2y = -1) → 3x
+ 2y = -10
|To make the x-coefficients
opposites, multiply the
transformed second equation
Add the equations.
When the result is a false statement, the graphs of the equations never
intersect. The graph confirms that the lines are parallel and have no points
This system has no solution because the lines never intersect.
The system is inconsistent. (It has no solution.)
The equations of the system are independent. (Their graphs are not
Solving a Linear System: Special Cases
When using either substitution or elimination, if both variables are
eliminated there are two possible outcomes:
â€¢ If the resulting equation is an identity, such as 5 = 5, then the
The system has infinitely many solutions.
The solutions may be stated as the set of all points on the line.
â€¢ If the resulting equation is a false statement, such as 0 = 4, then
the lines are parallel and never intersect.
The system has no solution.
The system is inconsistent and the equations are independent.