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Wednesday, September 11 th Please complete the warm up 

Wednesday, September 11 th Please complete the warm up . What is the slope and y intercept? -2x + 5y = 15 2. Describe each graph X= 5 y= -6. Ticket to Go Answers. Homework Answers. Y = 2x – 1 and y = -3x + 3. What went wrong?. Y = 2x – 1 and y = -3x + 3.

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Wednesday, September 11 th Please complete the warm up 

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  1. Wednesday, September 11th Please complete the warm up  What is the slope and y intercept? -2x + 5y = 15 2. Describe each graph X= 5 y= -6

  2. Ticket to Go Answers

  3. Homework Answers

  4. Y = 2x – 1 and y = -3x + 3 What went wrong?

  5. Y = 2x – 1 and y = -3x + 3 Where is the solution?

  6. What do we do!?!?!? Since we can’t just “estimate” this specific point, we will use something called: SUBSTITUTION

  7. Substitution • Good News….You already know how to do this! • Substitution is when you replace a known value for an equivalent quantity. • Examples of substitution in real life: • A recipe calls for ground beef and you substitute ground turkey • When Jay Cutler is a being a baby, they have to substitute in a different player

  8. Solving Systems of Equations by Substitution Remember Steps in math our like recipes. If you follow them….you’ll have a delicious ending!! Solve for one variable in at least one equation, if necessary Substitute the resulting expression into the other equation (circle and point to where substitution occurs) Solve that equation Substitute the value into one of the original equations and solve Write the values from Steps 3 and Steps 4 as an ORDERED PAIR (x,y)

  9. Helpful Hints • You can solve for x OR y • Only ONE equation needs to be solved for • Use inverse operations correctly: • Addition with subtraction • Division with multiplication 4. You should be SUBSTITUTING twice 5. CHECK YOUR ANSWERS!!!

  10. Just Watch First! Step 4:y=2x y=2(5) y=10 Substitute found value into EITHER of the equations Step 5: (5,10) Write the solution as an ordered pair y=2x y=x+5 Step 1: Done (both equations are solved for y Step 2: y=x+5 2x=x+5 I put 2x in for y since y=2x Step 3: -x from both sides x=5

  11. Step 2 y = x – 2 3x = x – 2 Step 3 –x –x 2x = –2 2x = –2 2 2 x = –1 Example #1 Solve the system by substitution y = 3x y =x – 2 Step 1y = 3x Both equations are solved for y. y = x – 2 Substitute 3x for y in the second equation. Solve for x. Subtract x from both sides and then divide by 2.

  12. Step 4 y = 3x y = 3(–1) y = –3 Step 5 (–1, –3) y = 3x y = x –2 –3 3(–1) –3 –1– 2   –3 –3 –3 –3 Write one of the original equations. Substitute –1 for x. Write the solution as an ordered pair. Check Substitute (–1, –3) into both equations in the system.

  13. Step 2 4x + y = 6 4x+(x + 1) = 6 Step 3 –1 –1 5x = 5 5x = 5 5 5 x = 1 Example #2 y =x + 1 4x + y = 6 The first equation is solved for y. Step 1y = x + 1 Substitute x + 1 for y in the second equation. 5x + 1 = 6 Simplify. Solve for x. Subtract 1 from both sides. Divide both sides by 5.

  14. Step 4 y = x + 1 y = 1 + 1 y = 2 Step 5 (1, 2) y = x + 1 4x + y = 6 2 1 + 1 4(1)+ 2 6 2 2  6 6  Write one of the original equations. Substitute 1 for x. Write the solution as an ordered pair. Check Substitute (1, 2) into both equations in the system.

  15. You Try! 2x + y = -4 X + y = -7

  16. + 2x +2x y = 2x + 8 Step 2 3x + 2y = 9 3x+ 2(2x + 8) = 9 Example #5 Show all 5 steps! –2x + y = 8 Solve by substitution. 3x + 2y = 9 Step 1–2x + y = 8 Solve the first equation for y by adding 2x to each side. Substitute 2x + 8 for y in the second equation. 3x + 2(2x + 8) = 9 Distribute 2 to the expression in parenthesis.

  17. –16 –16 7x = –7 7x = –7 77 Beeeeeee Careful! Step 3 3x + 2(2x) +2(8) = 9 Simplify. Solve for x. 3x + 4x + 16 = 9 7x + 16 = 9 Subtract 16 from both sides. Divide both sides by 7. x =–1

  18. Step 4 –2x + y = 8 –2 –2 y = 6 Almost Done! Write one of the original equations. –2(–1) + y = 8 Substitute –1 for x. y + 2 = 8 Simplify. Subtract 2 from each side. Step 5 (–1, 6) Write the solution as an ordered pair.

  19. Real World Application

  20. Steal of a Deal! Drewis deciding between two cell-phone plans. The first plan has a $50 sign-up fee and costs $20 per month. The second plan has a $30 sign-up fee and costs $25 per month. After how many months will the total costs be the same? What will the costs be? If Jenna has to sign a one-year contract, which plan will be cheaper? Explain. Write an equation for each option. Let t represent the total amount paid and m represent the number of months.

  21. + Option 1 t = $50 m $20 $30 $25 Option 2 t + = m Step 1 t = 50 + 20m t = 30 + 25m Step 2 50 + 20m = 30 + 25m Setting it Up Total paid sign-up fee for each month. payment amount is plus Both equations are solved for t. Substitute 50 + 20m for t in the second equation.

  22. Step 3 50 + 20m = 30 + 25m –20m – 20m –30–30 20 = 5m 5 5 m =4 Step 4 t = 30 + 25m t = 30 + 100 t = 130 Solve for m. Subtract 20m from both sides. 50 = 30 + 5m Subtract 30 from both sides. 20 = 5m Divide both sides by 5. Write one of the original equations. t = 30 + 25(4) Substitute 4 for m. Simplify.

  23. Write the solution as an ordered pair. Step 5 (4, 130) In 4 months, the total cost for each option would be the same $130. If Drew has to sign a one-year contract, which plan will be cheaper? Explain. Option 1: t = 50 + 20(12) = 290 Option 2: t = 30 + 25(12) = 330 Drew should choose the first plan because it costs $290 for the year and the second plan costs $330.

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