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# Alg1 8.2 Substitution Method

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### Alg1 8.2 Substitution Method

1. 1. Algebra 1 Lesson 8.2 Substitution Method
2. 2. Whadda ya know 'bout... Substitution Method
3. 3. how much does each item cost? \$3.50 fries = \$1.50 burger= \$1 \$7.50
4. 4. Goal: Use substitution to solve a system of linear equations.
5. 5. What does it mean to... "solve a system of linear equations?" answer: find the solution(s) y = 4x - 4 y = -2x + 8 the point that is a solution to both lines in the point of intersection, (2,4)
6. 6. Figure out the solution by using the guess and check method! System of equations: 2x + y = 20 x + y = 16 the only point that is true for both equations is (4.12) x 0 1 2 3 4 y 20 18 16 14 12
7. 7. Figure out the solution by using the guess and check method! System of equations: 3x - 4y = 17 x = 2y + 5
8. 8. A.E. I.N. SUBSTITUTION P. METHOD, FTW! L.F.
9. 9. Types of solutions: One Solution No Solutions Different slope Same slope Infinitely Many Solutions Different y-inter. Different y-inter. Same slope ordered pair false statement Same y-inter. identity
10. 10. How to subsitute System of equations: 3x - 4y = 17 x = 2y + 5 substitute find y: SMOTD 3(2y + 5) - 4y = 17 6y + 15 - 4y = 17 2y + 15 = 17 2y = 2 y=1 find x: x = 2y + 5 x = 2(1) + 5 x=2+5 x=7 answer: (7,1)
11. 11. How to substitute substitute SMOTD Isolate one variable and substitute into... Equation ivse-solvse Equation eev-say-sol-vee-say Solve for unknown variable and substitute into...
12. 12. System of equations: One solution (ordered pair) 3x = 2y - 6 x - y = -1 3(y-1) = 2y - 6 3y - 3 = 2y - 6 3x = 2y - 6 y - 3 = -6 3x = 2(-3) - 6 y = -3 3x = -6 - 6 3x = -12 answer: (-4,-3) x = -4
13. 13. System of equations: No Solution (false statement) 8x - 4y = 6 2x - y = 9 8x - 4y = 6 8x - 4(2x-9) = 9 8x - 8x + 36 = 9 36 = 9 FALSE STATEMENT- no solution
14. 14. System of equations: Infinitely Many (identity) 3y - 6x = 24 8 + 2x = y 3(8 + 2x) - 6x = 24 24 + 6x - 6x = 24 24 + 0 = 24 24 = 24 IDENTITY- infinitely many solutions