Solving Systems of Equations (by Substitution) Section 7.1 Solving Systems of Equations (by Substitution)

Objective By following instructions students will be able to: Use the method of substitution to solve systems of equations in two variables. Solve systems of equations graphically. Use systems of equations to model and solve real-life problems.

Systems of Equations When solving a systems of linear equation, there are three methods to choose from to find the point of intersection. Graphing (slope intercept form). Substitution (isolate a variable). Elimination (additive inverse).

Example 1: Solve the system of equations.

Example 2: A total of $12,000 is invested in two funds paying 9% and 11% simple interest. The yearly interest is $1180. How much is invested at each rate?

Example 3: Solve the system of equations.

Example 4: Solve the system of equations.

U-TRY #1 Solve. 1) 3) 2) 4)

Example 5: Solve the system by graphing.

Example 6: A small business invests $10,000 in equipment to produce a product. Each unit of the product cost $0.65 to produce and is sold for $1.20. How many items must be sold before the business breaks even?

Example 7: From 1990 to 1997, the population of Arizona was increasing at a faster rate than the population of Alabama. Two models that approximate the populations P (in thousands) are where t=0 represents 1990. According to these two models, when would you expect the population of Arizona to have exceeded the population of Alabama?

U-TRY #2 Solve either by graphing or algebraically. 1) 2)

Revisit Objective Did we… Use the method of substitution to solve systems of equations in two variables? Solve systems of equations graphically? Use systems of equations to model and solve real-life problems?

Homework Pg 495#s 1-65 EOO