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Graphing Linear Equations: Systems & Inequalities

Learn to solve linear systems by graphing in slope-intercept form, with a focus on interpreting graphical solutions and understanding linear inequalities. Master definitions and steps for solving systems graphically. Practice and check your answers for accuracy.

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Graphing Linear Equations: Systems & Inequalities

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  1. Bell Work 1/28/15 Graph the equation.

  2. Yesterday’s Homework • Any questions? • Please pass your homework to the front. • Make sure the correct heading is on your paper. • Is your NAME on your paper? • Make sure the homework is 100% complete. • Incomplete work will NOT be accepted.

  3. Next Chapter • Chapter 6 • Systems of Equations and Inequalities

  4. Heading 1/5/2020 Solving Systems by Graphing (y = mx+b) TSWBAT: solve a linear system by graphing when in slope-intercept form. Students solve a system of two linear equations in two variables algebraically and are able to interpret the answer graphically. Students are able to solve a system of two linear inequalities in two variables and to sketch the solution sets.

  5. Notes • Definitions • Linear System (or System of Equations) = Two or more equations with the same variables • Solution of a Linear System = The point where the two lines cross/intersect. -Must make BOTH equations TRUE! • Point of Intersection = The solution of the linear system.

  6. Notes • Solving a System of Equations by Graphing 1. Write each equation into slope-intercept form. What is m and b? m = move b = beginning 2. Graph both equations in the same coordinate plane. 3. Find the point of intersection. 4. Check your answer. - Plug that point into both equations and make sure that it is true for both.

  7. Notes Solve the system by graphing. Ex. 1) Put in slope- intercept form. 2) Graph the equations. - Find m and b first. 3) Point of intersection? 4) Check answer!

  8. Notes Step 5- Check your answer. x y

  9. Notes Now you try. Solve the system by graphing. Ex. 1) Put in slope- intercept form. 2) Graph the equations. - Find m and b first. 3) Point of intersection? 4) Check answer!

  10. Notes Step 5- Check your answer. x y

  11. Notes Solve the system by graphing. Ex. 1) Put in slope- intercept form. 2) Graph the equations. - Find m and b first. 3) Point of intersection? 4) Check answer!

  12. Notes Step 5- Check your answer. x y

  13. Notes Now you try. Solve the system by graphing. Ex. 1) Put in slope- intercept form. 2) Graph the equations. - Find m and b first. 3) Point of intersection? 4) Check answer!

  14. Notes Step 5- Check your answer. x y

  15. Notes • Number of Solutions for a Linear System C A B No solution One solution Infinite solutions (Same Lines) (Parallel Lines)

  16. Notes Solve the system by graphing. Ex. 1) Put in slope- intercept form. 2) Graph the equations. - Find m and b first. 3) Point of intersection? 4) Check answer!

  17. Summary • To solve a linear system by ________ first graph each equation separately. Next identify the __________ of both lines and circle it. That ordered pair is the _______ to the system. Check your answer by plugging it back into the ______ of equations. • graphing • intersection • solution • system

  18. Today’s Homework • Rules for Homework • Pencil ONLY. • Must show all of your work. • NO WORK = NO CREDIT • Must attempt EVERY problem. • Always check your answers.

  19. Homework 6.1A Solve the system by graphing.

  20. Ticket Out the Door • Complete the Ticket Out the Door without talking!!!!! • Talking = time after the bell! • Put your NAME on the paper. • When finished, turn your paper face DOWN. • Solve the system by graphing.

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