Graph and classify each system of equations. Find the solution/s if any. 1. y = x + 4 y + x = 4 2. ½ x + y = 2 2y + x = 4 3. y = -4x + 10 2x + ½y = 6 Use.

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Presentation transcript:

Graph and classify each system of equations. Find the solution/s if any. 1. y = x + 4 y + x = 4 2. ½ x + y = 2 2y + x = 4 3. y = -4x x + ½y = 6 Use substitution to solve each system of equations. 4. y + 2x = 1 x + y = 3 5. x - 10y = 2 x – 6y = 6 6. x +y + z = 5 2x – 3y + z = -2 4z = 8

Lesson 3.2 Solving Systems by Elimination

 Solve a system of two linear equation in two variables by elimination.

 You can model real-world situations involving two variables, such as business cost and revenue, with a system of two equations in two variables.

3 rd method to solve a system of equations. Use elimination to solve the system. EXAMPLE #1: 2x +5y = 15 -4x + 7y = -13 2(2x + 5y = 15) ** Multiply by 2.** -4x + 7y = -13 4x + 10y = 30 -4x + 7y = -13**Combine.** 17y = y = 1 Substitute y into either equation to get x. 2x + 5(1) = 15 2x + 5 = 15 2x = 10 x = 5 The solution is (5,1) The elimination method involves multiplying and combining the equations in a system in order to eliminate a variable.

The solution is (6,-4)  2x + y = 8 x – y = 10 The solution is (3,1)  p + q = 4 2p + 3q = 9

Use elimination to solve the system. 2x + 5y = 12 2x + 5y = 15 ** The lines are parallel. Therefore, it has no solutions.**

Example #3:  ** The lines coincide. Therefore, the system has an infinite number of solutions.** Use elimination to solve the system of equations. 2x +5y = 15Hint: Multiply the 1 st equation by 3 and the -3x – 7.5y = nd equation by 2 to eliminate the x.

 The Smith and Klein families went out to dinner. The Smith family had 6 hamburgers and 4 drinks, and the Klein family had 9 hamburgers and 7 drinks. The Smith family spent $18 and the Klein family spent $ How much does a drink cost?

 A laboratory technician is mixing a 10% saline solution with a 4% saline solution. How much of each solution is needed to make 500 milliliters of a 6% saline solution?

Lesson 3.2Page 169 (10-30 EVENS, 46, EVENS)