1. Solving Systems by Substitution Unit 6 Day 1

2. Identifying Number of Solutions You can determine the number of solutions of a linear system by: Writing both equations in slope intercept form Comparing slopes and y-intercepts –If slopes are different, one solution (lines intersect) –If slopes are same but y-intercepts are different, no solution (parallel lines) –If slopes are same AND y-intercepts are same, infinitely many solutions (same line)

3. Examples Determine the number solutions for the following linear systems a)5x+y=-2 -10x-2y=4 Slope Eq. 1: __ Y-int Eq.1: __ Slope Eq. 2: __ Y-int Eq.2: __ 5x+y = -2-10x -2y = 4 -5x -5x +10x +10x y = -5x-2 -2y = 10x + 4 /-2 /-2 /-2 y = -5x - 2 -5-2 -5 -2 Same Slope Same Y-Int Infinitely Many Solutions

4. Examples b) 6x+2y=3 6x+2y=-5 Slope Eq. 1: __ Y-int Eq.1: __ Slope Eq. 2: __ Y-int. Eq.2: __ 6x + 2y = 36x + 2y = -5 -6x -6x 2y = -6x+3 2y = -6x - 5 /2 /2 /2 /2 /2 /2 y = -3x + 3/2 y = -3x -5/2 -3 3/2 -3-5/2 Same Slope. Different Y-Intercepts No Solution

5. YOU TRY! a)b)c) d)e)f) One Solution No Solution Infinitely Many Solutions No Solution One Solution Infinitely Many Solutions

6. Solving by Substitution Steps: 1.Solve one equation for y or x (which-ever requires less steps  Remember what we did Friday??) 2.Substitute the solved equation into the other equation. 3.Solve the multi-step equation. 4.Substitute in the solution to either equation and solve for remaining variables. *Note: If both equations are solved for the same variable  Just set them equal and solve! Then do Step 4.

7. Examples 1)y = 4x + 8 y = -x – 7 **already both solved for y. 4x + 8 = -x – 7 +x +x 5x + 8 = - 7 - 8 -8 5x = -15 /5 /5 x = -3 y = -(-3) – 7 y = 3 – 7 y = -4 Solution is (-3,-4)

8. Examples 2) 3y + 2x = 4 x = -6y – 7 **one is already solved for x. 3y + 2(-6y – 7) = 4 3y -12y -14 = 4 -9y – 14 = 4 + 14 +14 -9y = 18 /-9 /-9 y = -2 x = -6(-2) -7 x = 12 – 7 x = 5 Solution is (5,-2)

9. Examples 2) 2x + y = 6 7x -8y = 113 **neither is solved. Solving for y is easiest. 2x + y = 6 -2x y = -2x + 6 7x -8(-2x + 6) = 113 7x + 16x - 48 = 113 23x – 48 = 113 + 48 +48 23x = 161 /23 /23 x = 7 y = -2(7) + 6 y = -14 + 6 y = -8 Solution is (7,-8)

10. YOU TRY!! Hint: C(n) is just like using y. 4) 5) n = -.5 or -1/2 C(n) = -4.5 or -9/2 (2, 3)

11. Homework Page 6 #2-7 and #15-20