1. System of equations and Inequalities….! By Cory Hunter

2. SYSTEM OF INEQUALITIES GRAPH A system of inequalities is a set of two or more inequalities with the same variables, graphed in the same coordinate plane.

3. SYSTEM OF INEQUALITIES PowerPoint

4. System of Equation Substitution Elimination

5. Solving by graphing Step 1: 4y = x – 12 [Equation 1.] Step 2: y = 1/4x – 3 [Rewrite in slope intercept form.] Step 3: y + x = 2 [Equation 2.] Step 4: y = - x + 2 [Rewrite in slope intercept form.] Step 5: Graph the two equations using the slope and y-intercept. Step 6: It appears that the two lines intersect at the point (4, - 2). Step 7: Check the solution: - 2 = 1/4(4) – 3 [Substitute the values in y = 1/4x - 3.] Step 8: - 2 = - 2 [Simplify.] Step 9: - 2 = - 4 + 2 [Substitute the values in y = - x + 2.] Step 10: - 2 = - 2 [Simplify.] Step 11: So, (4, - 2) is the solution of the linear system.

6. Elimination Elimination is the process of eliminating one of the variables in a system of equations using addition or subtraction in different ways with multiplication or division and solving the system of equations.

7. Elimination Example 1: x - y = 5 and 3x + 2y = 15 Multiply the first equation by 2 so that the coefficient of the y-terms in the system will be opposites. Then, add the equations and solve for x. 2(x - y) = 2(5) 2x - 2y = 10 3x + 2y =15 () 3x + 2y =15 5x = 25 x = 5 x - y = 5 Use the first equation. 5 - y = 5 Substitute 5 for x. -y = 0 ⇒ y = 0 The solution to this system is (5, 0)

8. Substitute To solve a system of equations by substitution… 1.Solve one equation for one of the variables. 2.Substitute the value of the variable into the other equation. Simplify and solve the equation. 4.Substitute back into either equation to find the value of the other variable.

9. Example 1 2p + 3q = 2 p - 3q = -17 Notice that neither equation is solved for a variable. Since p in the second equation does not have a coefficient, it will be easier to solve. p - 3q = -17 p = 3q – 17 Substitute the value of p into the first equation, and solve. 2p + 3q = 2 2(3q – 17) + 3q = 2 6q – 34 + 3q = 2 9q – 34 = 2 9q = 36 q = 4 Substitute Examples 1

10. References http://www.glencoe.com/sec/math/algebra/algebra1/algebra1_0 5/studyguide/pdfs/alg1_pssg056.pdf Algebra 2 Online! www.google.com http://www.icoachmath.com/math_dictionar y/Elimination_Method.html