7.2 Solving Systems of Equations by Substitution

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8-2: Solving Systems of Equations using Substitution

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7.2 Solving Systems of Equations by Substitution

Warm Up - Solve by Graphing y = –2x – 1 y = x + 5 2x + y = 4 (-2,3) is the solution (3, -2) is the solution

Steps for Solving by Substitution Solving Systems of Equations by Substitution Step 2 Step 3 Step 4 Step 5 Solve for one variable in one equation. Step 1 Substitute the resulting expression into the other equation. Now solve that equation to get the value of the first variable. Substitute that value into either one of the original equations and solve for the other variable. Write the values from steps 3 and 4 as an ordered pair, (x, y), and check.

Example One y = x + 1 4x + y = 6

Example Two x + 2y = –1 x – y = 5

Example Three 2x + y = –4 x + y = –7

Example Four - No Solution or Infinite Solutions y = 3x + 2 6x - 2y = -4 2x + 2y = 8 x + y = -2

Example Five - Real-Life Application The difference of two numbers is 40. Six times the smaller one minus the larger one is 5. What are the two numbers?

Example Six - Real-Life Application Tickets for the school play cost $6 for adults and $2 students. If 175 tickets are sold, with cash receipts of $750, how many student tickets were sold?