Lesson 7 3 Elimination Using Addition and Subtraction

Lesson 7 -3 Elimination Using Addition and Subtraction

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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 2 x + 3 y = 23 and -2 x + 8 y = 32 2 x + 3 y = 23 + -2 x + 8 y = 32 11 y = 55 y=5 2 x + 3(5) = 23 2 x = 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 4 x Two times the first number 2 x minus three times another number is 12. – 3 y = 12 added to three times the second number is 6. + 3 y = 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