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Bell Work 2/5/14 Solve the system by graphing. 1. 3x 2 y 12 x 2y 4 3x 2 y 12 3x 3x 2 y 3 x 12 2 2 2 3 y x6 2 3 m b6 2 x 2y 4 x x 2 y x 4 2 2 2 1 y x 2 2 1 m b2 2 2, 3 Yesterday’s Homework 1. Any questions? 2. Please pass your homework to the front. • Make sure the correct heading is on your paper. • Is your NAME on your paper? • Make sure the homework is 100% complete. • Incomplete work will NOT be accepted. Heading 5/24/2017 6.2A Solving Systems by Substitution (isolated) TSWBAT: solve a linear system by substitution when a term is already isolated. Students solve a system of two linear equations in two variables algebraically and are able to interpret the answer graphically. Students are able to solve a system of two linear inequalities in two variables and to sketch the solution sets. Notes • Solving a System of Equations by Substitution 1. Solve one of the equations for x or y. - Get x or y by itself. 2. Substitute your new expression from Step 1 into the other equation and solve for the variable. 3. Plug that solved variable into the other equation from Step 1 and solve for the other variable. 4. Check your answers by plugging it into the original equations. Notes Solve the system by substitution. Ex. The variable x is x 2 x y 5 already by itself. x y 5 2 y 5 2 2 y7 2, 7 1) Solve for x or y. 2) Substitute into other equation. 3) Plug in answer into other equation. 4) Check answer! Notes Now you try. Solve the system by substitution. Ex. The variable y is y4 x y 2 already by itself. x y 2 x 4 2 4 4 x6 6,6, 44 1) Solve for x or y. 2) Substitute into other equation. 3) Plug in answer into other equation. 4) Check answer! Notes Solve the system by substitution. Ex. The variable x is x3 2 x 5 y 1 already by itself. 2x 5 y 1 2 3 5 y 1 6 5y 1 6 6 5 y 5 5 5 y 1 3, 1 1) Solve for x or y. 2) Substitute into other equation. 3) Plug in answer into other equation. 4) Check answer! Notes Now you try. Solve the system by substitution. Ex. The variable y is y 1 3x 2 y 8 already by itself. 3x 2 y 8 3x 2 1 8 3x 2 8 2 2 3x 6 3 3 x2 2, 1 1) Solve for x or y. 2) Substitute into other equation. 3) Plug in answer into other equation. 4) Check answer! Notes Solve the system by substitution. Ex. The variable y is y 2x x y 12 x y 12 x 2x 12 3x 12 3 3 x4 already by itself. Step 3 y 2x y 24 y 8 4,4, 88 1) Solve for x or y. 2) Substitute into other equation. 3) Plug in answer into other equation. 4) Check answer! Notes Now you try. Solve the system by substitution. Ex. The variable x is x 3 y 2 x 4 y 4 2 x 4 y 4 2 3 y 4 y 4 6 y 4 y 4 2 y 4 2 2 y2 already by itself. Step 3 x 3 y x 3 2 x 6 6, 2 1) Solve for x or y. 2) Substitute into other equation. 3) Plug in answer into other equation. 4) Check answer! Notes Solve the system by substitution. Ex. The variable x is x 2y 8 already by itself. 2 x 5 y 11 2 x 5 y 11 2 2 y 8 5 y 11 4 y 16 5 y 11 9 y 16 11 16 16 9 y 27 9 9 y 3 1) Solve for x or y. Step 3 x 2y 8 x 2 3 8 x 6 8 x2 2, 3 2) Substitute into other equation. 3) Plug in answer into other equation. 4) Check answer! Notes Solve the system by substitution. Ex. The variable y is y 3x 4 already by itself. 2 x 2 y 16 1) Solve for x or y. 2 x 2 y 16 2 x 2 3x 4 16 2x 6x 8 16 8x 8 16 8 8 8x 24 8 Now you try. 8 x 3 Step 3 y 3x 4 y 3 3 4 y 94 y 5 3,3, 55 2) Substitute into other equation. 3) Plug in answer into other equation. 4) Check answer! Notes Solve the system by substitution. Ex. The variable y is y 4x 6 already by itself. y 2x 4 y 2x 4 4x 6 2x 4 2x 2x 2x 6 4 6 6 2x 10 2 2 x 5 1) Solve for x or y. Step 3 y 4x 6 y 4 5 6 y 20 6 y 14 5, 14 2) Substitute into other equation. 3) Plug in answer into other equation. 4) Check answer! Notes Solve the system by substitution. Ex. The variable y is y 3x 5 already by itself. y 4x 2 y 4x 2 3x 5 4x 2 3x 3x 5 7 x 2 2 2 7 7x 7 7 1 x Now you try. 1) Solve for x or y. Step 3 y 3 x 5 y 3 1 5 y 35 y 2 1, 2 2) Substitute into other equation. 3) Plug in answer into other equation. 4) Check answer! Summary substitution first To solve a linear system by ___________ identify the isolated variable in one of the equations. _______ equations to Next plug that expression into the other _________ find the value of one variable. Finally plug that equations to find the solution into any of the original _________ other variable. Today’s Homework Rules for Homework 1. Pencil ONLY. 2. Must show all of your work. • NO WORK = NO CREDIT 3. Must attempt EVERY problem. 4. Always check your answers. Homework 6.2A Solve the system by substitution. x 3 x 4 1. 2. x y 8 2 x 3 y 2 4. y 2x x y 9 7. x 2 y 5 3x 4 y 5 5. x 4 y x y 15 8. 3. y 3 4 x 2 y 14 6. y 3x 2 x 4 y 14 y 3x 1 2 x 4 y 16 Ticket Out the Door Complete the Ticket Out the Door without talking!!!!! Talking = time after the bell! Put your NAME on the paper. When finished, turn your paper face DOWN. Solve the system by substitution. x 3 2 x 4 y 10