Lesson Plan-Grade 10
Lesson Title: Solving systems of equations
State Standards: MA.912.A.3.14 : Solve systems of
linear equations and inequalities in two and three variables using graphical, substitution,
and elimination methods.
Grade : 10 (FCAT)
Subject: Mathematics
Objectives:
1. Student
can identify the system of equations and also predict solution set (as
consistent , inconsistent and dependent )
- Student can solve consistent
equations by selecting appropriate substitution or elimination method.
- Students focus on finding solutions to situations found in everyday
life.
Recapitulation (10 mins)
The student needs to recall the types of equations.
Explanation: (40 mins)
Activity 1: Explain
classification of system of equations
In a1x+b1y+c1=0,
a2x+b2y+c2=0
if a1/a2 ≠ b1/b2 ≠ c1/c2. Then they are consistent
if a1/a2
= b1/b2 ≠ c1/c2.Then they are inconsistent
if a1/a2
= b1/b2 = c1/c2.Then they are dependent
Consistent
equations have unique solution
Inconsistent equations have no solution
Dependent
equations have infinite solutions
The student needs to identify
given set of equations to be consistent or
inconsistent or dependent.
Activity 2: The Student understands to
classify and solve the given set of equations using substitution method.
Example:
3x+2y=8,
2x+3y=7 now by substituting x=(7-3y)/2 in 3x+2y=8Student gets the solution set as
x=2, y=1.
Activity 3 : Student
learns the elimination method to solve
linear system of equations.
Example
x + y =5 – (1)
X – y = 1 - (2)
by adding equ (1) and (2) variable
y can be eliminated. Then we will get x= 3, and y=2.
Activity 4: Student translates the given
word problem into system of equations and finds out the solution set equations
from word problems
For example: A small business
invests $10,000 in equipment to produce a product. Each unit of the product costs $0.65 to produce and is
sold for $ 1.20 .How many items must be sold before the business breaks even?
The total cost of producing x
units is
Total cost = Cost per
unit*Number of units + Initial cost
C= 0.65x+10,000
The revenue obtained by
selling x units is
Total revenue = price per unit
* Number of units
R =1.2x
Because the break even point
occurs when R=C, you have
1.2x =0.65x+10,000
0.55x= 10,000
X= 18,182 units
Recapitulation and Evaluation: (10 mins)
- Solve the simultaneous
equations by elimination method
x + y=6, x-y =2
- Solve the simultaneous
equations by substitution method 7x-6y=15,6x+7y =25
- You are offered two different
jobs selling dental supplies.
- one company offers a
straight commission of 6% of sales.
- The other company offers a
salary of $ 250 per week plus 3%
of sales
How much would you have to sell in a week in order to make
the straight commission offer better?
