1. I can graph an equation in two variables and identify pairs as its solutions.( A. REI.10)

Ex. Graph the equation: 2x-y = 1In a T – table present 6 solution of this equation. What are the solutions that represent the y- intercept and the x- intercept?

2. I can determine if the linear system has an unique solution, has multiple solutions or no solutions.

Ex. Without graphing, decide if the system has infinite solutions, no solution or one solution

y = 2x + 3-2x + y = 1

x+ 2y = -72x – 3y =0

y = 2x + 3-4x + 2y = 6

Determine the value of h and k for which the system has no solutions.

-y +h = 2x4x- ky = 3

3. I can graph a linear system and identify its solution.(A.REI. 6)

Ex. Solve by graphing the following system.

3x + y = 32x – y = 7

4. I can algebraically solve a linear system by elimination method.(A.REI. 5)

Ex. Which order pair (x, y) satisfy the system of equations shown below?

-3x +5y = 76x – 10y = -14

5. I can algebraically solve a linear system by substitution method.(A.REI. 6)

Ex. Solve the following system by substitution.

4x + 3y = 62x – y = 7

6. I can write equations in two variables and use them to solve problems. Graph the equations on coordinates axes with labels and scales( A. CED. 2 and A.REI.6)

Ex. In a certain game, a player can solve easy or hard puzzles. A player earns 30 points for solving an easy puzzle and 60 points for solving a hard puzzle. Tina solved a total of 50 puzzles playing this game, earning 1950 points in all. How many hard puzzles did Tina solve?

7. I can graph the solution to a linear inequality in two variables ( A.REI.12)

Ex. Graph the following inequality

-5y + 2x > -5

8. I can graph the solution to a system of linear inequalities. (A.REI.12)

Ex. Solve the following system on inequalities

2x + y < 1-y +3x < 1

9. I can interpret solutions as viable or non- viable options for a system of inequalities. ( A.CED. 3)

Ex. Solve the following system of inequalities and check if (2, -2) is a solution of the systemy< -2x +3y >= x -4

11. I can use the constraints represented by inequalities or system on inequalities to find the set of (x, y) that maximizes or minimizes the objective function and find the maximum and/or minimum values(A.CED. 3)

Ex. For the previous problem find how many trays of each type of muffin should the baker make to maximize his profit. What is the maximum profit that that he can make.

10. I can represent constraints by inequalities or system of inequalities and graph it to find the feasible region(A.CED. 3)

Ex. Find the objective function for the following problem and solve it.

Baking a tray of corn muffins takes 4c milk and 3c wheat flour. A tray of bran muffins takes 2c milk and 3c wheat flour. A baker has 16c milk and 15c wheat flour. He makes $3 profit per tray of corn muffins and $2 profit per tray of bran muffins.

11. I can identify the point(s) of intersection of y = f(x) and y = g(x) as the solution of the system.

( A.REI.D.11)

Which of the points A-F are the solution of the system

y = f(x)

y = g(x)

Explain how you know.

Choose one of the points which is not a solution to the system and explain why is not a solution to the system.

12. I can solve a system consisting of a linear equation and a quadratic equation in two variables algebraically and graphically.

y = 2x2 + 3xy = -2x +7.

Find all the solutions of this system algebraically and represent them on a graph.

Key:1. y = 2x -1

y int

x int

2. These are parallel line( have the same slope); therefore, the system has no solutionThese two lines do not have the same slope; therefore these two lines intersect and the system has one solutionThese two lines overlap; therefore the system has infinite solutionk = -2, h = 1.5

3.

4. Infinite solutions5. X = 2.7 and y = -1.66. X = 35 and y =157.

x y0 -12 3-1 -30.5 03 5

8.

9.

( 2, -2) is part of the solution because is part of the overlapped shaded area

9. 4x + 2y ≤ 163x + 3y ≤ 15P = 3x + 2y maximize

10.

When x = 3 and y = 2 the profit is maximum 13.

11. B, C, E, F are solutions of the system, because all represent points where f(x) intercepts g(x) or f(x)= g(x)

12. A is not a solution because it only belongs two one function and not the other.

13. (1, 5) and (-3.5, 14)