System of equations and Inequalities….!

By Cory Hunter

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.

SYSTEM OF INEQUALITIES

PowerPoint

9.5: Graphing and Solving Systems of Inequalities

Intro: Systems of inequalities are similar to systems of equations. A solution is still an ordered pair that is true in both statements.

The graphing is a little more harder - it’s all about the shading.

System of Equation

Substitution Elimination

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.

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• 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.

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.

Elimination Example 1: x - y = 5 and 3x + 2y = 15Multiply the first equation by 2 so that the coefficientof the y-terms in the system will be opposites. Then,add the equations and solve for x.

2(x - y) = 2(5) 2x - 2y = 103x + 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)

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.

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 = -17p = 3q – 17

Substitute the value of p into the first equation, and solve.2p + 3q = 22(3q – 17) + 3q = 26q – 34 + 3q = 29q – 34 = 29q = 36 q = 4

Substitute Examples 1

References

• http://www.glencoe.com/sec/math/algebra/algebra1/algebra1_05/studyguide/pdfs/alg1_pssg056.pdf

• Algebra 2 Online! • www.google.com• http://www.icoachmath.com/

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