This handout accompanies an introduction to solving systems of linear equations. A system of linear equations is made of 2 or more linear equations. I...
This handout accompanies an introduction to solving systems of linear equations. A system of linear equations is made of 2 or more linear equations. In Algebra I you will solve a system of 2 equations. The solution of a system of linear equations is an ordered pair that satisfies both equations. The solution is a point that is on the graph of both lines.
#4 Solve the system of equations.
y = 2x – 4 y=5–x
We will solve the system by graphing. Graphing Calculator Method: Enter the equations in y= . Press ZOOM 6 to view in the standard window. Press 2nd TRACE
5
ENTER ENTER ENTER
The intersection point is displayed. This is the solution of the system. (3, 2)
Graph By Hand Method: Graph by making a table of values for each equation. Plot points from the tables on graph paper. Use a straight edge to sketch each graph. Locate the intersection point which is the solution.
Solve Systems of Equations – Graphing Method Three Ways Linear Equations Are Related 1. ___________________ in one point. The intersection point represents the ____________ of the system. 2. ___________________ in all points. The graphs are the _____________. ___________________ number of solutions.
3. Lines do not ____________________ The lines are ___________________ There is ________ solution.
4. Solve the system of equations.
5. Solve the system of equations.
6. Solve each system of equations. A. y = 3x – 4 y = 2x
7. Tickets to the football game were $8.00 for adults and $5.00 for students. A total of 360 tickets were sold for total receipts of $2514.00. How many student tickets were sold? Which of the following systems of equations could be used to solve this problem?
A. x + y = 360 8x + 5y = 2514
C. x + y = 2514 8x + 5y = 360
B. x + y = 360 x + y = 2514
D. 8x + 5y = 360 8x + 5y = 2514
8. What is the value of y in the solution of the following system of linear equations? y = 3x + 11 2x + 3y = 0 A. –3
B.
–2
C. 2
D. 3
9. Which of the following graphs shows the solution to the system of linear equations? 2x + 2y = 12 y = 3x + 2 A.
Solve Systems of Equations – Graphing Method Three Ways Linear Equations Are Related 1. _Intersect___________ in one point. The intersection point represents the _solution__ of the system. 2. __Intersect________ in all points. The graphs are the _same_______. ___Infinite______ number of solutions.
3. Lines do not __intersect______. The lines are __parallel________. There is __no___ solution.
7. Tickets to the football game were $8.00 for adults and $5.00 for students. A total of 360 tickets were sold for total receipts of $2514.00. How many student tickets were sold? Which of the following systems of equations could be used to solve this problem?
C. x + y = 360 8x + 5y = 2514
C. x + y = 2514 8x + 5y = 360
D. x + y = 360 x + y = 2514
D. 8x + 5y = 360 8x + 5y = 2514
8. What is the value of y in the solution of the following system of linear equations? y = 3x + 11 2x + 3y = 0 B. –3
B.
–2
C. 2
D. 3
9. Which of the following graphs shows the solution to the system of linear equations? 2x + 2y = 12 y = 3x + 2 B.
