Solving Systems of Equations Using the Elimination Method.

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Solving Systems of Equations

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Solve Systems of Equations by Elimination

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Presentation transcript:

Solving Systems of Equations Using the Elimination Method

Solving Systems of Equations Using Elimination Elimination is when you solve for one variable by adding, subtracting, or multiplying to the original equations. These equations often have both variables in them and are NOT in slope-intercept form.

Elimination using Addition Solve the systems of equations x - 2y = 5 2x + 2y = 7 REMEMBER: We are trying to find the Point of Intersection. (x, y) Lets add both equations to each other

Elimination using Addition Consider the system…what makes it different than the other systems we just solved for? x - 2y = 5 2x + 2y = 7 Lets add both equations to each other + NOTE: We use the Elimination Method, if we can immediately cancel out two like terms.

Elimination using Addition Consider the system x - 2y = 5 2x + 2y = 7 Lets add both equations to each other + 3x = 12 x = 4  ANS: (4, y) NOTE: We use the Elimination Method, if we can immediately cancel out two like terms.

Elimination using Addition Consider the system x - 2y = 5 2x + 2y = 7 ANS: (4, y) Lets substitute x = 4 into this equation y = 5Solve for y - 2y = 1 y = 1 2  NOTE: We use the Elimination Method, if we can immediately cancel out two like terms.

Elimination using Addition Consider the system x - 2y = 5 2x + 2y = 7 ANS: (4, ) Lets substitute x = 4 into this equation y = 5Solve for y - 2y = 1 y = 1 2  1 2 NOTE: We use the Elimination Method, if we can immediately cancel out two like terms.

Elimination using Addition Solve the System of Equations 3x + y = 14 4x - y = 7 NOTE: We use the Elimination Method, if we can immediately cancel out two like terms.

Elimination using Addition Consider the system 3x + y = 14 4x - y = 7 7x= 21 x = 3  ANS: (3, y) +

Elimination using Addition Consider the system ANS: (3, ) 3x + y = 14 4x - y = 7 Substitute x = 3 into this equation 3(3) + y = y = 14 y = 5 5  NOTE: We use the Elimination Method, if we can immediately cancel out two like terms.

Elimination using Multiplication Solve the System of Equations 6x + 11y = -5 6x + 9y = x + 20y = -8When we add equations together, nothing cancels out

Elimination using Multiplication Consider the system 6x + 11y = -5 6x + 9y = -3

Elimination using Multiplication Consider the system 6x + 11y = -5 6x + 9y = ( )

Elimination using Multiplication Consider the system - 6x - 11y = 5 6x + 9y = y = 2 y = -1 ANS: (x, ) 

Elimination using Multiplication Consider the system 6x + 11y = -5 6x + 9y = -3 ANS: (x, ) y = -1 Lets substitute y = -1 into this equation 6x + 9(-1) = -3 6x + -9 = x = 6 x = 1 

Elimination using Multiplication Consider the system 6x + 11y = -5 6x + 9y = -3 ANS: (, ) y = -1 Lets substitute y = -1 into this equation 6x + 9(-1) = -3 6x + -9 = x = 6 x = 1 1 

Elimination using Multiplication Solve the System of Equations x + 2y = 6 3x + 3y = -6 Multiply by -3 to eliminate the x term

Elimination using Multiplication Consider the system x + 2y = 6 3x + 3y = ( )

Elimination using Multiplication Consider the system -3x + -6y = -18 3x + 3y = y = -24 y = 8 ANS: (x, 8) 

Elimination using Multiplication Consider the system x + 2y = 6 3x + 3y = -6 ANS: (x, 8) Substitute y = 8 into equation y =8 x + 2(8) = 6 x + 16 = 6 x = -10 

Elimination using Multiplication Consider the system x + 2y = 6 3x + 3y = -6 ANS: (, 8) Substitute y = 8 into equation y =8 x + 2(8) = 6 x + 16 = 6 x = 

Solve the System of Equations x + 2y = 5 2x + 6y = 12 ANS: (3,1 ) You Try This One! It is more of an application problem.

You Write A Problem We will work some shortly. Try and make it reasonable difficult.