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Warm Up Solve for the indicated variable. 1. P = R – C for R 2. V = Ah for A

Systems of Equations. 11-6. 3 V. = A. 1. C – S. h. 3. t. Course 3. Warm Up Solve for the indicated variable. 1. P = R – C for R 2. V = Ah for A 3. R = for C. R = P + C. Rt + S = C. Systems of Equations. 11-6. Course 3.

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Warm Up Solve for the indicated variable. 1. P = R – C for R 2. V = Ah for A

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  1. Systems of Equations 11-6 3V = A 1 C – S h 3 t Course 3 Warm Up Solve for the indicated variable. 1.P = R – C for R 2.V = Ah for A 3.R = for C R = P + C Rt + S = C

  2. Systems of Equations 11-6 Course 3 Learn to solve systems of equations. Vocabulary system of equations solution of a system of equations

  3. Systems of Equations 11-6 Caution! When solving systems of equations, remember to find values for all of the variables. Course 3 A system of equations is a set of two or more equations that contain two or more variables. A solution of a system of equations is a set of values that are solutions of all of the equations. If the system has two variables, the solutions can be written as ordered pairs.

  4. Systems of Equations 11-6 Caution! When solving systems of equations, remember to find values for all of the variables. Course 3 • A system of equations can be solved three ways: • Graphically • Substitution • Elimination

  5. Systems of Equations 11-6 Course 3 Additional Example 1A: Solving Systems of Equations by GRAPHING Solve the system of equations. y = 4x – 6 y = x + 3 Graph both equations. The solution is where the two lines intersect.

  6. Systems of Equations 11-6 Course 3 Additional Example 1A: Solving Systems of Equations by SUBSTITUTION Solve the system of equations. y = 4x – 6 y = x + 3 The expressions x + 3 and 4x – 6 both equal y. So by the Transitive Property they equal each other. y= 4x – 6 y =x + 3 4x – 6 = x + 3

  7. Systems of Equations 11-6 Course 3 Additional Example 1A Continued Solve the equation to find x. 4x – 6 = x + 3 – x– x Subtract x from both sides. 3x - 6 = 3 + 6+ 6 Add 6 to both sides. 3x9 Divide both sides by 3. 3 = 3 x = 3 To find y, substitute 3 for x in one of the original equations. y = x + 3 = 3 + 3 = 6 The solution is (3, 6).

  8. Systems of Equations 11-6 Course 3 Additional Example 1B: Solving Systems of Equations by ELIMINATION y = 2x + 4 y = 2x + 4 y = -2 + 4x y = 4x - 2 1. Line up the equations by x, y, and constants. 2. Eliminate one of the variables by changing the coefficient. The solution of the system of equations is (3, 10).

  9. Systems of Equations 11-6 Helpful Hint You can solve for either variable. It is usually easiest to solve for a variable that has a coefficient of 1. Course 3

  10. Systems of Equations 11-6 1 2 ( , 2) Course 3 Insert Lesson Title Here Try This! Solve each system of equations using the given method. 1. y = 5x + 10 y = –7 + 5x 2.y = 2x + 1 y = 4x 3. 6x – y = –15 2x + 3y = 5 4. Two numbers have a sum of 23 and a difference of 7. Find the two numbers. no solution By graphing By substitution (–2,3) By elimination 15 and 8 Any method

  11. Systems of Equations 11-6 Course 3 Insert Lesson Title Here Homework: Workbook pg. 88 *Practice using all 3 methods.

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