All equations must be solved by the same values of x and y 1 System Word Problems, Elimination, Substitution, & Graphs Systems of Equations – More than one equation All equations must be solved by the same values of x and y

----- Meeting Notes (5/2/17 09:40) ----- three methods how to find the x and y's that work in all the equations will do one problem three ways to find x and y

1 System Word Problems, Elimination, Substitution, & Graphs Tom is 3 times as old as Todd. In 5 years Tom’s age will be 3 years more than 2 times as old as Todd. How old is Todd?

Write equations to represent the information given. 1 System Word Problems, Elimination, Substitution, & Graphs Tom is 3 times as old as Todd. In 5 years Tom’s age will be 3 years more than 2 times as old as Todd. How old is Todd? Substitution Write equations to represent the information given.

Write equations to represent the information given. 1 System Word Problems, Elimination, Substitution, & Graphs Tom is 3 times as old as Todd. In 5 years Tom’s age will be 3 years more than 2 times as old as Todd. How old is Todd? Substitution Write equations to represent the information given. Tom = 3(Todd)

Write equations to represent the information given. 1 System Word Problems, Elimination, Substitution, & Graphs Tom is 3 times as old as Todd. In 5 years Tom’s age will be 3 years more than 2 times as old as Todd. How old is Todd? Substitution Write equations to represent the information given. Tom = 3 (Todd) Tom + 5 = 2(Todd + 5) + 3

Replace Tom with 3(Todd) in second equation. 1 System Word Problems, Elimination, Substitution, & Graphs Tom is 3 times as old as Todd. In 5 years Tom’s age will be 3 years more than 2 times as old as Todd. How old is Todd? Substitution Replace Tom with 3(Todd) in second equation. Tom = 3 (Todd) Tom + 5 = 2(Todd + 5) + 3 3 (Todd) + 5 = 2(Todd + 5) + 3

1 System Word Problems, Elimination, Substitution, & Graphs Tom is 3 times as old as Todd. In 5 years Tom’s age will be 3 years more than 2 times as old as Todd. How old is Todd? Substitution Solve for Todd, 3 (Todd) + 5 = 2(Todd + 5) + 3

3 (Todd) + 5 = 2(Todd + 5) + 3 3(Todd) + 5 = 2(Todd) + 10 + 13 1 System Word Problems, Elimination, Substitution, & Graphs Tom is 3 times as old as Todd. In 5 years Tom’s age will be 3 years more than 2 times as old as Todd. How old is Todd? Substitution Solve for Todd, then Tom 3 (Todd) + 5 = 2(Todd + 5) + 3 3(Todd) + 5 = 2(Todd) + 10 + 13 Todd = 8 years old

1 System Word Problems, Elimination, Substitution, & Graphs Tom is 3 times as old as Todd. In 5 years Tom’s age will be 3 years more than 2 times as old as Todd. How old is Todd? Substitution Solve for Todd, then Tom Todd = 8 years old Tom = 3 (Todd) Tom = 3(8) = 24 years old

Put Tom and Todd on the left side and the constants on the right. 1 System Word Problems, Elimination Substitution, & Graphs Tom is 3 times as old as Todd. In 5 years Tom’s age will be 3 years more than 2 times as old as Todd. How old is Todd? Elimination Put Tom and Todd on the left side and the constants on the right. Tom = 3(Todd) Tom – 3(Todd) = 0

Tom + 5 = 2(Todd + 5) + 3 Tom + 5 = 2(Todd) + 10 + 3 1 System Word Problems, Elimination Substitution, & Graphs Tom is 3 times as old as Todd. In 5 years Tom’s age will be 3 years more than 2 times as old as Todd. How old is Todd? Elimination Put Tom and Todd on the left side and the constants on the right. Tom + 5 = 2(Todd + 5) + 3 Tom + 5 = 2(Todd) + 10 + 3 Tom - 2(Todd) = 8

Add or subtract the equations to eliminate Tom or Todd. 1 System Word Problems, Elimination Substitution, & Graphs Tom is 3 times as old as Todd. In 5 years Tom’s age will be 3 years more than 2 times as old as Todd. How old is Todd? Elimination Add or subtract the equations to eliminate Tom or Todd. Tom - 2(Todd) = 8 Tom – 3(Todd) = 0

Add or subtract the equations to eliminate Tom or Todd. 1 System Word Problems, Elimination Substitution, & Graphs Tom is 3 times as old as Todd. In 5 years Tom’s age will be 3 years more than 2 times as old as Todd. How old is Todd? Elimination Add or subtract the equations to eliminate Tom or Todd. Tom + 2(Todd) = 8 - Tom – -3(Todd) = 0 Todd = 8

1 System Word Problems, Elimination Substitution, & Graphs Tom is 3 times as old as Todd. In 5 years Tom’s age will be 3 years more than 2 times as old as Todd. How old is Todd? Elimination And solve for Tom Todd = 8 years old Tom = 3 (Todd) Tom = 3(8) = 24 years old

Replace Tom and Todd with x and y. Let Todd = x Let Tom = y 1 System Word Problems, Elimination Substitution, & Graphs Tom is 3 times as old as Todd. In 5 years Tom’s age will be 3 years more than 2 times as old as Todd. How old is Todd? Graphing Replace Tom and Todd with x and y. Let Todd = x Let Tom = y

Replace Tom and Todd with x and y. Let Todd = x Let Tom = y 1 System Word Problems, Elimination Substitution, & Graphs Tom is 3 times as old as Todd. In 5 years Tom’s age will be 3 years more than 2 times as old as Todd. How old is Todd? Graphing Replace Tom and Todd with x and y. Let Todd = x Let Tom = y Tom = 3 (Todd) y = 3 x

Tom + 5 = 2(Todd + 5) + 3 y + 5 = 2(x + 5) + 3 1 System Word Problems, Elimination Substitution, & Graphs Tom is 3 times as old as Todd. In 5 years Tom’s age will be 3 years more than 2 times as old as Todd. How old is Todd? Graphing Replace Tom and Todd with x and y. Let Todd = x Let Tom = y Tom + 5 = 2(Todd + 5) + 3 y + 5 = 2(x + 5) + 3

Write in slope-intercept form and graph y + 5 = 2 (x+5) + 3 1 System Word Problems, Elimination Substitution, & Graphs Tom is 3 times as old as Todd. In 5 years Tom’s age will be 3 years more than 2 times as old as Todd. How old is Todd? Graphing Write in slope-intercept form and graph y + 5 = 2 (x+5) + 3 y = 2x + 10 + 3 – 5 y = 2x + 8

y (x,y) = (8,24) x Graphing y = 3 x y = 2x + 8 1 System Word Problems, Elimination Substitution, & Graphs Graphing y = 3 x y = 2x + 8 (x,y) = (8,24) Let Todd = x 8 years old Let Tom = y 24 years old x

1 System Word Problems, Elimination Substitution, & Graphs

Later in the week = 4th method : matrices