Solving Systems of Equations Using the Elimination Method
- Slides: 23
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 - 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 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 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 + 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 + 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 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 x - y = 7 7 x = 21 x=3 ANS: (3, y)
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 = -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 x + 9 y = -3
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 = 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 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 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 3 x + 3 y = -6 Multiply by -3 to eliminate the x term
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 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 + 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 + 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 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 reasonable difficult.
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