7.4 – SOLVING SYSTEMS OF LINEAR EQUATIONS USING A SUBSTITUTION STRATEGY

Systems of Linear Equations

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

Substitution Strategy

Example

“expression for x”

Example

Example

Example

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

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%

Substitution strategy

Example

Example

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