Solving Systems by Graphing PDF

Unit: Systems Name _____________________________________ Student Handout 2 Date _____________________________Pd______ SOLVING SYSTEMS BY GRAPHING When solving a system of equations by graphing, it’s oft...

Unit: Systems Name _____________________________________ Student Handout 2 Date _____________________________Pd______ SOLVING SYSTEMS BY GRAPHING When solving a system of equations by graphing, it’s often easiest if both equations are written in _________ - _________________ form. In A and B below, graph to solve the system. Then answer a-b. A y = 2x − 1 B y = -x − 2 -4x + 2y = 4 6x + 6y = -12 a. What did you notice about the lines in A? What does this mean? b. What did you notice about the lines in B? What does this mean? The following types of solutions are possible when solving a system of linear equations: ______ SOLUTION ______ SOLUTION ____________ MANY y Lines have the y y Lines have Lines have same ________ different the same and different x x __________ x ________ y-intercepts; and intersect and same they do not at _____ point. y-intercept. intersect. Solve each system of equations by graphing. 1 3 1. y = 2x + 4 2. y = 2x x+y=7 -x + 2y = -8 ©Maneuvering the Middle LLC, 2020 Solution: Solution: 3. Solve the system of equations by graphing. 3x + 6y = -12 and 2y = -x − 4 4. The graphed line below represents an 5. Tish believes that the linear equations equation in a system with no solution. Write a shown do not have a solution because they do possible second not intersect. equation in the Do you agree? system. Explain. 6. Circle the names of the two students whose equations would have infinitely many solutions. Explain your choice. PENNY RAVI COURTNEY EDWIN 2x − y = -1 2x + 3y = 3 -4x − 6y = -6 6x + 6y = 9 7. Abbie bought a combination of streamers and balloons for a birthday party. The number of balloons, y, was three less than two times the amount of streamers purchased, x. If Abbie bought a combination of 9 balloons and streamers, the following system can represent the situation: x+y=9 and y = 2x − 3 Solve the system by graphing and find the number of each item Abbie purchased. Summarize today’s lesson: ©Maneuvering the Middle LLC, 2020