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Lesson 7-3 Elimination Using Addition and Subtraction Click the mouse button or press the Space Bar to display the answers. Objectives • Solve system of equations by using elimination with addition • Solve system of equations by using elimination with subtraction Vocabulary • Elimination - the use of addition or subtraction to eliminate one variable and solve a system of equations Solve Systems of Equations: Elimination • Sometimes we can add (or subtract) two sets of equations together and eliminate a variable • We can do this because we are adding (or subtracting) the same thing (since they are equal) from both sides of the equation • Example: Solve 2x + 3y = 23 and -2x + 8y = 32 2x + 3y = 23 + -2x + 8y = 32 11y = 55 y=5 2x + 3(5) = 23 2x = 8 x=4 (equation one) (equation two) Eliminate x by adding Divide both sides by 11 Sub y= into equation one Simplifying Divide both sides by 3 Example 1 Use elimination to solve the system of equations. Since the coefficients of the x terms, –3 and 3, are additive inverses, you can eliminate the x terms by adding the equations. Write the equation in column form and add. Notice that the x value is eliminated. Divide each side by –2. Simplify. Example 1 cont Now substitute –15 for y in either equation to find the value of x. First equation Replace y with –15. Simplify. Add 60 to each side. Simplify. Divide each side by –3. Simplify. Answer: The solution is (–24, –15). Example 2 Four times one number minus three times another number is 12. Two times the first number added to three times the second number is 6. Find the numbers. Let x represent the first number and y represent the second number. Four times one number 4x Two times the first number 2x minus three times another number is 12. – 3y = 12 added to three times the second number is 6. + 3y = 6 Example 2 cont Use elimination to solve the system. Write the equation in column form and add. Notice that the y value is eliminated. Divide each side by 6. Simplify. Example 2 cont Now substitute 3 for x in either equation to find the value of y. First equation Replace x with 3. Simplify. Subtract 12 from each side. Simplify. Divide each side by –3. Simplify. Answer: The numbers are 3 and 0. Example 3 Use elimination to solve the system of equations. Since the coefficients of the x terms, 4 and 4, are the same, you can eliminate the x terms by subtracting the equations. Write the equation in column form and subtract. Notice that the x value is eliminated. Divide each side by 5. Simplify. Example 3 cont Now substitute 2 for y in either equation to find the value of x. Second equation Simplify. Add 6 to each side. Simplify. Divide each side by 4. Simplify. Answer: The solution is (6, 2). Summary & Homework • Summary: – Sometimes adding or subtracting two equations will eliminate one variable • Homework: – Pg 385 12-24 even, 30, 32