Do Now 121119 Take out HW from last

Do Now 12/11/19 Ø Take out HW from last night. l Ø Copy HW in your planner. l Ø Text p. 245, #9 -18 all, 20 & 27 Text p. 251, #4 -22 evens, 31 In your notebook, answer the following question. A farmer plants corn and wheat on a 180 -acre farm. The farmer wants to plant three times as many acres of corn as wheat. Write a system of linear equations that represents this situation. How many acres of each crop should the farmer plant? x= y=

A farmer plants corn and wheat on a 180 -acre farm. The farmer wants to plant three times as many acres of corn as wheat. Write a system of linear equations that represents this situation. How many acres of each crop should the farmer plant? x + y = 180 x= x = 3 y y=

Homework Text p. 245, #9 -18 all, 20 & 27

Homework Text p. 245, #9 -18 all, 20 & 27

Learning Goal Ø Students will be able to write and graph systems of linear equations. Learning Target l Students will be able to solve systems of linear equations by elimination

Section 5. 1 “Solve Linear Systems by Graphing” Linear System– consists of two more linear equations. x + 2 y = 7 3 x – 2 y = 5 Equation 1 Equation 2 A solution to a linear system is an ordered pair (a point) where the two linear equations (lines) intersect (cross).

Section 5. 2 “Solve Linear Systems by Substitution” Solving a Linear System by Substitution (1) Solve one of the equations for one of its variables. (When possible, solve for a variable that has a coefficient of 1 or -1). (2) Substitute the expression from step 1 into the other equation and solve for the other variable. (3) Substitute the value from step 2 into the revised equation from step 1 and solve.

“Solve Linear Systems by Substituting” Equation 1 Equation 2 x – 2 y = -6 4 x + 6 y = 4 x = -6 + 2 y 4 x 4(-6+ +6 y 2 y) = 4+ 6 y = 4 -24 + 8 y + 6 y = 4 -24 + 14 y = 4 y =2 x – 2 y = -6 Equation 1 x = -6 + 2(2) x = -2 (-2) - 2(2) = -6 -6 = -6 Substitute value for x into the original equation The solution is the point (-2, 2). Substitute (-2, 2) into both equations to check. 4(-2) + 6(2) = 4 4=4

During a football game, a bag of popcorn sells for $2. 50 and a pretzel sells for $2. 00. The total amount of money collected during the game was $336. Twice as many bags of popcorn sold compared to pretzels. How many bags of popcorn and pretzels were sold during the game? y = 2 x x= $2. 50 y + $2. 00 x = $336 y= 96 bags of popcorn and 48 pretzels

“How Do You Solve a Linear System? ? ? ” (1) Solve Linear Systems by Graphing (5. 1) (2) Solve Linear Systems by Substitution (5. 2) (3) Solve Linear Systems by ELIMINATION!!! (5. 3)

Section 5. 3 “Solve Linear Systems by Elimination” Ø ELIMINATIONadding or subtracting equations to obtain a new equation in one variable. Solving Linear Systems Using Elimination (1) Multiply the whole equation by a constant in order to be able to eliminate a variable. (2) Add or Subtract the equations to eliminate one variable. (3) Solve the resulting equation for the other variable. (4) Substitute in either original equation to find the value of the eliminated variable.

“Solve Linear Systems by Elimination” ADDITION Eliminated Equation 1 Equation 2 + 2 x + 3 y = 11 -2 x + 5 y = 13 8 y = 24 y=3 2 x + 3 y = 11 Equation 1 2 x + 3(3) = 11 2 x + 9 = 11 x=1 2(1) + 3(3) = 11 11 = 11 Substitute value for y into either of the original equations The solution is the point (1, 3). Substitute (1, 3) into both equations to check. -2(1) + 5(3) = 13 13 = 13

“Solve Linear Systems by Elimination” Eliminat ed Equation 1 Equation 2 _ + 4 x + 3 y = 2 -5 x 5 x + -3 y 3 y ==-2 2 -x = 4 x = -4 4 x + 3 y = 2 Equation 1 4(-4) + 3 y = 2 -16 + 3 y = 2 y=6 4(-4) + 3(6) = 2 2=2 ION T C A R T B SU Substitute value for x into either of the original equations The solution is the point (-4, 6). Substitute (-4, 6) into both equations to check. 5(-4) + 3(6) = -2 -2 = -2

“Solve Linear Systems by Elimination” Eliminat ed Equation 1 Equation 2 + 8 x - 4 y = -4 -3 x 4 y + = 4 y 3 x = + 14 5 x 8 x - 4 y = -4 Equation 1 8(2) - 4 y = -4 16 - 4 y = -4 y=5 8(2) - 4(5) = -2 -2 = -2 Arrange like terms = 10 x= 2 Substitute value for x into either of the original equations The solution is the point (2, 5). Substitute (2, 5) into both equations to check. 4(5) = 3(2) + 14 20 = 20

On Your Own 4 x – 3 y = 5 -2 x + 3 y = -7 7 x – 2 y = 5 7 x – 3 y = 4 3 x + 4 y = -6 2 y = 3 x + 6 (-1, -3) (1, 1) (-2, 0)

“Solve Linear Systems by Elimination Multiplying First!!” First Eliminated Equation 1 Equation 2 6 x + 5 y = 19 x (-3) 2 x + 3 y = 5 + 6 x + 5 y = 19 -6 x – 9 y = -15 -4 y = 4 y = -1 2 x + 3 y = 5 Equation 2 2 x + 3(-1) = 5 2 x - 3 = 5 x=4 6(4) + 5(-1) = 19 19 = 19 Substitute value for y into either of the original equations The solution is the point (4, -1). Substitute (4, -1) into both equations to check. 2(4) + 3(-1) = 5 5=5

“Solve Linear Systems by Elimination Multiplying First!!” Eliminated Equation 1 Equation 2 x (-2) 2 x + 5 y = 3 3 x + 10 y = -3 + -4 x - 10 y = -6 3 x + 10 y = -3 -x 2 x + 5 y = 3 Equation 1 2(9) + 5 y = 3 18 + 5 y = 3 y = -3 2(9) + 5(-3) = 3 3=3 First = -9 x=9 Substitute value for x into either of the original equations The solution is the point (9, -3). Substitute (9, -3) into both equations to check. 3(9) + 10(-3) = -3 -3 = -3

“Solve Linear Systems by Elimination Multiplying First!!” Eliminated Equation 1 Equation 2 4 x + 5 y = 35 x (2) -3 x + 2 y = -9 x (-5) + 8 x + 10 y = 70 15 x - 10 y = 45 23 x 4 x + 5 y = 35 Equation 1 4(5) + 5 y = 35 20 + 5 y = 35 y=3 4(5) + 5(3) = 35 35 = 35 First = 115 x=5 Substitute value for x into either of the original equations The solution is the point (5, 3). Substitute (5, 3) into both equations to check. -3(5) + 2(3) = -9 -9 = -9

“Solve Linear Systems by Elimination Multiplying First!!” Eliminated Equation 1 Equation 2 9 x + 2 y = 39 x (2) 6 x + 13 y = -9 x (-3) + First 18 x + 4 y = 78 -18 x - 39 y = 27 -35 y = 105 y = -3 9 x + 2 y = 39 Equation 1 9 x + 2(-3) = 39 9 x - 6 = 39 x=5 Substitute value for y into either of the original equations 9(5) + 2(-3) = 39 The solution is the point (5, -3). Substitute (5, -3) into both 39 = 39 equations to check. 6(5) + 13(-3) = -9 -9 = -9

Guided Practice x+y=2 2 x + 7 y = 9 6 x – 2 y = 1 -2 x + 3 y = -5 (1, 1) (-0. 5, -2) 3 x - 7 y = 5 9 y = 5 x + 5 (-10, -5)

A business with two locations buys seven large delivery vans and five small delivery vans. Location A receives five large vans and two small vans for a total cost of $235, 000. Location B receives two large vans and three small vans for a total cost of $160, 000. What is the cost of each type of van? 2 x + 5 y = 235, 000 3 x + 2 y = 160, 000 x= y= (30, 000, 35, 000) $30, 000 for a small van and $35, 000 for a large van.

Homework Text p. 251, #4 -22 evens, 31