1. Ch. 7 – Matrices and Systems of Equations 7.2 - Elimination

2.  Ex: Solve the system.  Since both equations are in Ax + By = C form, use elimination.  Multiply each equation by a number to get opposite variable amounts  Because there are an opposite amount of y’s, we will add the equations together to cancel the y’s!  Solve the remaining equation for x to get…  x=1. But we need an answer in the form of (x, y)…  I still need a y, so plug 1 in for x and solve for y!  y=2, so the answer is (1, 2)! 7() 2( ) Elimination

3. Solve the system: 1. (6, 3) 2. (-3, 6) 3. (-18, 11) 4. (-5, 3) 5. No Solution 6. Infinite Solutions

4. Solve the system: 1. (5, 2) 2. (6, -1.5) 3. (10, -1) 4. (0, 5) 5. No Solution 6. Infinite Solutions

5. Solve the system: 1. (0, 7/3) 2. (7, 0) 3. (7/4, 7/4) 4. (5, 3) 5. No Solution 6. Infinite Solutions

6.  Ex: Al has 19 coins, all dimes or quarters. The total amount of change he has is $2.65. How many dimes does Al have?  We have 2 variables (# dimes and # quarters), so set up a system of equations!  1 st eqn: the total number of coins…  2 nd eqn: the total cost of the coins…  Solve by elimination!  So d = 14!  Answer: 14 dimes -.25( )

7.  If a calculator is allowed, solve any system of equations by graphing!  Ex: Solve this system by graphing.  Solve both equations for y…  …then graph and find all intersections!  Answer: (7.991, 1.019)