Post on 15-Dec-2015
Todays Objectives
• Solve problems that involve systems of linear equations in two variables, graphically and algebraically, including:• Explain a strategy to solve a system of linear
equations• Solve a problem that involves a system of linear
equations• Determine and verify the solution of a system
of linear equations algebraically
Solving a system of linear equations algebraically
• In the last lesson, you solved linear systems by graphing• This strategy is time consuming and you
can only approximate the solution• We can use algebra to determine an
exact solution• In the next two lessons we will look at two
strategies that use algebra to solve linear systems:• Substitution Strategy• Elimination Strategy
Example
• Create a linear system to model this situation:• Mr. Mennie invested $2000, part at an annual interest rate of
8%, and the rest as an annual interest rate of 10%. After one year, the total interest was $190
• How much money did Mr. Mennie invest at each rate?
• Solution: Given: Linear System
2 investments Let x dollars represent the amount invested at 8%Let y dollars represent the amount invested at 10%
Total investment is $2000
x+y = 2000
x dollars at 8% Interest is 8% of x = 0.08x
y dollars at 10% Interest is 10% of y = 0.10y
Total interest is $190 0.08x + 0.10y = 190
Example
• Create a Linear System to model this situation:• Mr. Nishi invested $1800, part at an annual
interest rate of 3.5%, the rest at 4.5%. After one year, the total interest was $73.• How much did Mr. Nishi invest at each rate?• Solution: x + y = 1800 (1) 0.035x + 0.045y = 73 (2)
Mr. Nishi invested $800 at 3.5% and $1000 at 4.5%