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Geometric

Copyright 2005 Edwin Ellis

Graph the linear equations on the same coordinate plane.

If the lines intersect, the solution is the point of intersection.

If the lines are parallel, there is no solution.

If the lines coincide, there is infinitely many solutions.

Solve one of the linear equations for one of the variables (look for a coefficient of one).

Substitute this variables value into the other equation.

Solve the new equation for the one remaining variable.

Substitute this value into one of the original equations and find the remaining variable value.

Look for variables with opposite or same coefficients.

If the coefficients are opposites, add the equations together. If the coefficients are the same, subtract the equations, by changing the sign of each term in the 2nd equation and adding.

Substitute the value of the remaining variable back into one of the orig. equations to find the other variable.

Choose a variable to eliminate.

Look the coefficients and find their LCD. This is the value you are trying to get.

Multiply each equation by the needed factor to get the LCD.

Continue as for regular elimination

GRAPHING

SUBSTITUTION

ELIMINATION

ELINIMATION VIA MULTIPLICATIONThe solution (if it has just one) is an ordered pair. This point is a solution to both equations and will test true if substituted into each equation.

Method 1Method 4Method 3Method 2SUMMARYSolving Systems of Linear EquationsFinding solutions for more than one linear equation by using one of four methods.