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Page (2,1), (-2,0), (6,9) 2. (0,-2), (5,1) 3. (0,0) 4. (0,3), (-5,4) 5. (-5,0), (-2,-2) 6. x + y ≤10

12)C = number of chocolate bars L = amount of licorice 1500C L ≤ )H=number of days at the Hyatt L = number of days at Lotte H + L ≤ 12 13) X=number of pens Y=number of pencils

Solving Systems of Equations by Graphing A SYSTEM OF EQUATIONS is a group of two or more equations. When the system of equations are lines, they are called linear systems. A solution of a system of linear equations in two variables is an ordered pair (x,y) that is a solution to each equation.

In order to find the solution, you graph both lines and see where they intersect. The point where they intersect is their solution. No Solution when both lines are parallel (same slope, different y-intercepts) Infinite Number of Solutions when both lines are the same lines (same slope and same y- intercept) INFINITELY MANY SOLUTIONS In order to determine if a point is a solution, substitute it into the equations and see if it is true.

Example Solve the system by graphing: y=x+2 y=-2x+2

(a) (b) (c) (d)

Two or more linear inequalities make a system of linear inequalities The solutions of a system of inequalities are all the points that satisfy both inequalities. It is also represented by a shaded area and is the intersections or overlap of the two linear inequalities.

y<4x-1

y≥-4x-3

y≥-4x-3 and y<4x-1 The solution is the dark area where the graphs overlap

y≥-4x-3 and y<4x-1 The solution is the dark area where the graphs overlap

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