Math Pacing Elimination Using Addition and Subtraction 1.The sum of two numbers is 31. The greater number is 5 more than the lesser number. What are the two numbers? 2.Complementary angles have a sum of 90°. Angles A and B are complementary and the measure of angle A is 14 ° less than the measure of angle B. Find the measures of angles A and B. 3.What value of c in the system of equations 5x + y = – 1 and – 2y = 10x + c will produce a system of equations with infinitely many solutions? Let x = the greater number Let y = the lesser number Let x = the measure of  A Let y = the measure of  B

Elimination Using Addition and Subtraction

Sometimes adding two equations together will eliminate one variable. Using this step to solve a system of equations is called elimination.

Use elimination to solve the system of equations. Example 3-1a 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. Elimination Using Addition

Example 3-1a Now substitute –15 for y in either equation to find the value of x. Simplify. Add 60 to each side. Divide each side by –3. Simplify. First equation Replace y with –15. Simplify. Answer: The solution is (–24, –15). Elimination Using Addition

Example 3-1b Use elimination to solve the system of equations. Answer: (2, 1) Elimination Using Addition

Example 3-2a 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 minus three times another number is12. Two times the first number added to three times the second number is6. 4x4x – 3y3y = 12 2x2x + 3y3y = 6 Write and Solve a System of Equations

Example 3-2a Use elimination to solve the system. Notice that the y value is eliminated. Divide each side by 6. Simplify. Write the equation in column form and add. Write and Solve a System of Equations

Example 3-2a Now substitute 3 for x in either equation to find the value of y. Answer: The numbers are 3 and 0. First equation Replace x with 3. Simplify. Subtract 12 from each side. Simplify. Divide each side by –3. Simplify. Write and Solve a System of Equations

Example 3-2b Four times one number added to another number is –10. Three times the first number minus the second number is –11. Find the numbers. Answer: –3, 2 Write and Solve a System of Equations

Elimination Using Addition and Subtraction Sometimes subtracting one equation from another will eliminate one variable.

Example 3-3a`` 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. Elimination Using Subtraction Use elimination to solve the system of equations. –

Example 3-3a`` Now substitute 2 for y in either equation to find the value of x. Answer: The solution is (6, 2). Second equation Simplify. Add 6 to each side. Simplify. Divide each side by 4. Simplify. Elimination Using Subtraction

Example 3-3b Use elimination to solve the system of equations. Answer: The solution is (2, –6). Elimination Using Subtraction

Example 3-4a Multiple-Choice Test Item Ifandwhat is the value of y ? A (3, –8) B 3 C –8 D (–8, 3) Read the Test Item You are given a system of equations, and you are asked to find the value of y. Elimination Using Subtraction

Example 3-4a Solve the Test Item You can eliminate the y terms by subtracting one equation from the other. Write the equation in column form and subtract. Notice that the y value is eliminated. Divide each side by 14. Simplify. Elimination Using Subtraction

Example 3-4a Now substitute 3 for x in either equation to solve for y. Answer: C Notice that B is the value of x and A is the solution of the system of equations. However, the question asks for the value of y. First equation Simplify. Subtract 24 from each side. Simplify. Elimination Using Subtraction

Example 3-4b Multiple-Choice Test Item Ifandwhat is the value of x ? A 4 B (4, –4) C (–4, 4) D –4 Answer: D Elimination Using Subtraction