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5-2 Solving a System of Equations using Substitution Name _______________ HW: 5.2 pg. 285 #2-7 Guided Notes: Check that each ordered pair is a solution to a system. If the pair is not a solution, explain why not. Example 1: (3, –4) y = 2x – 10 & 3y = 15 – 9x Example 2: (2, -6) y = 2x – 10 Group Problems You try 1: (2, 3) y=5–x & 2y = x +4 & 2y = x +4 You try 2: (4, 1) & 3y = 15 – 9x y=5–x Guided Notes: How to solve an equation when Group Problems there are variables on both sides. Example 3: 2x + 1 = 5x – 9 You try 3: 5x + 10 = 15x – 20 Example 4: 7(x –1)+2 = 3x + 7 You try 4: 4(x –1) – 1 = 2x + 7 Guided Notes: How to solve an equation for a Group Problems variable. Example 5: Solve for x: Do x Undo = 3x + 6y = 12 Result You try 5: Solve for x: Do x Undo = 7x + 14y = 21 Result Multiply 3 Add 6y Example 6: Solve for y: 12 50x – 10y = 30 You try 6: Solve for y: Directed Notes: Solve a system of equations 15x – 5y = 30 Group Problems using substitution. Example 7: If both equations are already solved for the SAME variable, then all you need to do is to set the equations equal to each other. y = 2x – 10 You try 7: y=x+8 y = 20 – 2x Set equations equal to each other & solve for x. y = 5 – 3x After you have a value for x, solve for y by substituting your answer for x into the original equations. y = 2x – 10 y = 5 – 3x Solve for y by substituting the value for x into the original equations. y=x+8 y = 20 – 2x Directed Notes: Solve a system of equations using substitution. Example 8: Substitute one equation into the other and solve for x. y = 5x – 10 2y – 3x = 8 After you have a value for x, solve for y by substituting your answer for x into the original equations. y = 5x – 10 2y – 3x = 8 Directed Notes: Solve a system of equations using substitution. Example 9: Solve for one variable first (solve for y) 5y + 15x = 10 2y + 8x = 8 Group Problems You try 8: Substitute one equation into the other and then solve for x. y = 6 + 3x 3y – 5x = 10 Solve for y by substituting the value for x into the original equations. y = 6 + 3x 3y – 5x = 10 Group Problems Example 9: Solve for one variable first (solve for x) 6y – 3x = 12 3x + 2y = 12 Then substitute one equation into the other and solve for x. 2y + 8x = 8 Then substitute one equation into the other and solve for y. 3x + 2y = 12 After you have a value for x, solve for y by substituting your answer for x into the original equations. 5y + 15x = 10 2y + 8x = 8 After you have a value for y, solve for x by substituting your answer for y into the original equation. 6y – 3x = 12 3x + 2y = 12