Solving Systems of Linear Equations Graphing Substitution Elimination Using Addition Elimination Using Subtraction Elimination Using Multiplication Use if one of the variables has opposite coefficients in the two equations x - y = 9

7x + y = 7 Use if one of the two variables in either equation has a coefficient of 1 or -1 Use if none of the coefficients are 1 or -1 and neither of the variables

can be eliminated by simply adding or subtracting the equations 3x - 4y = -10

5x + 8y = -2 5x + 7y = 2

-2x + 7y = 9 Use if one of the variables has the same coefficient in the two equations Use to estimate solutions, since graphing usually does not give an exact solution. Or if both equations are in slope intercept form. y = -3x + 10

y = x - 2 5x - y = 17

3x + 2y = 5 Graph each equation on the coordinate plane

and determine the number of solutions. If one solution, the lines will intersect at one point. If many or infinite solutions, the lines will be the same. If no solution, the lines will be parallel. Solve one equation for the variable. Substitute the resulting expression into the other equation to replace the variable. Then solve the equation. Substitute the value of the variable into either original equation and solve for the other variable. Write the solution as an ordered pair. Elimination Write the system so like terms with the same or

opposite coefficients are aligned. Multiply at least one equation by a constant to get two equations that contain opposite terms. Add or subtract the equations, eliminating one

variable. Then solve the equation. Substitute the value of the variable into either of the equations and solve

for the other variable. Write your solution as an ordered pair. If you get a true statement, there are many solutions.

Ex. -3 = -3 If you get a false statement, there is no solution.

Ex. 2 = 5

"Elimination"

by Brad Becker, MD

Write the point of intersection as an ordered pair.

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# Solving Systems of Linear Equations

Helping students determine a method for and solve systems of linear equations.

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