System of equations and Inequalities

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

Substitute Examples 1

• 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

10
References

• http//www.glencoe.com/sec/math/algebra/algebra1/a
  lgebra1_05/studyguide/pdfs/alg1_pssg056.pdf
• Algebra 2 Online!
• www.google.com
• http//www.icoachmath.com/math_dictionary/Eliminat
  ion_Method.html