Pre-AP Pre-Calculus Chapter 7, Section 1 Solving Systems of Two Equations

The Method of Substitution You can solve a system of equations by substituting one equation into the other. What it does is “eliminates” a variable so you can solve for the other variable. The solution to a system of equations is an ordered pair, so once you find one of the variables, you must find the other one.

Using the Substitution Method

Solving a Nonlinear System by Substitution

Solving a Nonlinear System Algebraically

Solving Systems Graphically To solve a system graphically: The equations must be in y= format Type the equations into y1 and y2 Find the intersections of the graphs

The Method of Elimination To solve by elimination: First get the equations into standard form (easiest way) You will need to choose a variable and multiply the equation(s) by a number to make that variable have opposite coefficients Then just add the two equations and solve for the remaining variable.

Using the Elimination Method

Finding No Solution

Finding Infinitely Many Solutions

Applications U.S. Personal Consumption Expenditures YearDentists (billions of dollars) Health Insurance (billions of dollars)

Use the table from the previous slide to complete the following problem Find linear regression equations for the table for dentists and health insurance. Superimpose their graphs on a scatterplot of the data. Use the models to estimate when the U.S. Personal consumption expenditures for dentists will be the same as that for health insurance and the corresponding amount

Determining the Equilibrium Price

Ch 7.1 Homework Pg. 575 – 577, #’s: 2, 4, 7, 10, 22, 23, 28, 29, 36, 39, 44, 52, total problems, NO WORK = NO CREDIT Gray book: pg. 525