Solving Systems of Equations Using the Elimination Method

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Solving Systems of Equations Using the Elimination Method

Solving Systems of Equations Using the Elimination Method

Solving Systems of Equations Using Elimination • Elimination is when you solve for one

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 - 2 y = 5

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

Elimination using Addition Consider the system…what makes it different than the other systems we

Elimination using Addition Consider the system…what makes it different than the other systems we just solved for? x - 2 y = 5 + 2 x + 2 y = 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 - 2 y = 5 + 2

Elimination using Addition Consider the system x - 2 y = 5 + 2 x + 2 y = 7 = 12 3 x x=4 Lets add both equations to each other 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 - 2 y = 5 2 x

Elimination using Addition Consider the system x - 2 y = 5 2 x + 2 y = 7 4 - 2 y = 5 - 2 y = 1 y= 1 2 Lets substitute x = 4 into this equation. Solve for y 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 - 2 y = 5 2 x

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

Elimination using Addition Solve the System of Equations 3 x + y = 14

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

Elimination using Addition Consider the system 3 x + y = 14 + 4

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

Elimination using Addition Consider the system 3 x + y = 14 Substitute x

Elimination using Addition Consider the system 3 x + y = 14 Substitute x = 3 into this equation 4 x - y = 7 3(3) + y = 14 9 + y = 14 y=5 ANS: (3, 5 ) NOTE: We use the Elimination Method, if we can immediately cancel out two like terms.

Elimination using Multiplication Solve the System of Equations + 6 x + 11 y

Elimination using Multiplication Solve the System of Equations + 6 x + 11 y = -5 6 x + 9 y = -3 12 x + 20 y = -8 When we add equations together, nothing cancels out

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

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

Elimination using Multiplication Consider the system -1 (6 x + 11 y = -5

Elimination using Multiplication Consider the system -1 (6 x + 11 y = -5 ) 6 x + 9 y = -3

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

Elimination using Multiplication Consider the system + - 6 x - 11 y = 5 6 x + 9 y = -3 -2 y = 2 y = -1 ANS: (x, -1 )

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

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

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

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

Elimination using Multiplication Solve the System of Equations x + 2 y = 6

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

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

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

Elimination using Multiplication Consider the system + -3 x + -6 y = -18

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

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

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

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

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

You Try This One! It is more of an application problem. Solve the System

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

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

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