1 / 4

Objective: Solve systems of linear equations by substitution

Section 7-2 Solve Systems by Substitution SPI 23D: select the system of equations that could be used to solve a given real-world problem. Objective: Solve systems of linear equations by substitution. Three Methods of solving Systems of Equations: Solve by Graphing

sierra-roth
Download Presentation

Objective: Solve systems of linear equations by substitution

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Section 7-2 Solve Systems by SubstitutionSPI 23D: select the system of equations that could be used to solve a given real-world problem • Objective: • Solve systems of linear equations by substitution • Three Methods of solving Systems of Equations: • Solve by Graphing • Solve by Substitution • Solve by Elimination

  2. Solve a System of Linear Equations by Substitution Substitute: Replace a variable with an equivalent expression containing the other variable. Solve the system of linear equations using substitution. y = - 4x + 8 y = x + 7 x + 7 1. Write an equation containing only one variable. y = = - 4x + 8 Substitute x + 7 for y. 2. Solve the equation for x. x = 0.2 3. Substitute the x value into either equation to find y. y = x + 7 y = 0.2 + 7 = 7.2

  3. Solve a System of Linear Equations by Substitution Sometimes it is necessary to, first, solve one of the equations for a variable before using substitution. Solve the system of linear equations using substitution. 6y + 8x = 28 3 = 2x - y 1. Solve one of the equations for a variable. 3 = 2x – y 2x – 3 = y 2. Substitute the equation in step 1, into the remaining equation. 6y + 8x = 28 6 + 8x = 28 (2x – 3) 3. Solve for x. Substitute x into either equation to find y. x = 2.3 and y = 1.6

  4. Real-world and Systems of Equations Suppose you are thinking about buying a car. Car A cost $17,655 and you expect to pay an average of $1230 per year for fuel and repairs. Car B costs $15,900 and the average cost of fuel and repairs is $1425 per year. After how many years are the total costs for the cars the same? 1. Write two equations to model the problem. C(y)= 1425y + 15,900 C(y)= 1230y + 17,655 2. Use substitution to solve. 1230y + 17,655 = 1425y + 15,900 17,655 - 15,900 = 1425y - 1230y 17,655 - 15,900 = 1425y - 1230y 1755 = 195y 9 = y The cost will be the same after 9 years.

More Related