Check HW p 118 #1-6, 13, 14, 16, 17, 37, 56-60 (3,1) (2,1) 2. 1. 3. (-2,4) all reals no solution no solution one solution all reals Notes 3-2 Day 1: Solving Systems Algebraically Using Substitution & Elimination The lines intersect in ___ point The solution is __________ The lines intersect in _________ points The solution is __________ The lines intersect in __ points The solution is __________ Goal: Take two equations with two variables & create one equation with one variable which can then be solved using skills from pre-algebra & algebra. Examples: Solve the following systems using THE MOST EFFICIENT METHOD. Check your work. substitution or elimination? Why? Solution ________ substitution or elimination? Why? Solution ________ substitution or elimination? Why? Solution ________ substitution or elimination? Solution ________ substitution or elimination? Solution ________ substitution or elimination? Solution ________ substitution or elimination? Solution ________ Note on 2 special cases: If all variables are eliminated & the remaining statement is true, the solution is _________________. If all variables are eliminated & the remaining statement is false, the solution is ________________. Note on how to select the most efficient method to solve a system: When do we use substitution? _____________________________________________________ When do we use elimination? _____________________________________________________ Steps for Solving Systems Using Substitution: Step 1: Choose one of the equations and solve for either x or y. Step 2: Substitute the solution from step 1 into the other equation. Step 3: Solve this new equation. Step 4: Substitute the solution from step 3 and find the second variable. Steps for Solving Systems Using Elimination: Step 1: If necessary, multiply one or both equations by numbers so that adding like terms vertically will result in one variable being eliminated. You must have opposite coefficients for this to happen. Step 2: Add equations vertically. Step 3: Solve for the remaining variable. Step 4: Substitute the solution back in to solve for the second variable In teams, continue to work on the worksheet. Use the help stations posted on the boards. Homework Answers 1. (9,28) 2. (1,3) 3. (-9, 1/2) 4. (3,-2) 5. No solution 6. (-1,3/2) 7. (-3.75,3.5) or (-15/4,7/2) 8. infinitely many solutions 9. (3,2) 10. (-8,22/3) or (-8,7.3) Homework Answers 1. (9,28) 2. (1,3) 3. (-9, 1/2) 4. (3,-2) 5. No solution 6. (-1,3/2) 7. (-3.75,3.5) or (-15/4,7/2) 8. infinitely many solutions 9. (3,2) 10. (-8,22/3) or (-8,7.3)