Download 3.1 Solving Linear Systems by Graphing

3.1 Solving Linear Systems by
Graphing
Objective: solve a system of linear
equations in two variables by graphing
What are systems of linear equations?
Systems of Linear Equations
• A system of two linear equations in two variables x and
y consists of two equations. The coefficients of the
terms in the equations can be any real numbers
3x – y = 3
x + 2y = 8
Equation 1
Equation 2
• A solution of a system of two linear equations in two
variables is an ordered pair (x,y) that satisfies both
equations.
• When you graph the system, the solution is
represented by the point (or points) of intersection of
the two lines.
Solve a System by Graphing
y = -x +3
y = 2x + 9
Solve a System by Graphing
3x – y = 3
x + 2y = 8
Solve a System by Graphing
x – 3y = 1
-x + y = -1
Solutions of Systems
• It is also possible for a system to have
infinitely many solutions or no solution.
• You can find out how many solutions a linear
system has by graphing each equation and
analyzing the graphs.
Number of Solutions of a Linear
System
• Exactly One Solution:
– The graph of the system is a pair of lines that intersect in one point.
– the lines have different slopes
– the system has exactly one solution
• Infinitely Many Solutions:
– The graph of the system is a pair of identical lines
– The lines have the same slope and the same y-intercept
– The system has infinitely many solutions
• No Solution:
– The graph of the system is a pair of parallel lines
– The lines have the same slope and different y-intercepts
– The system has no solution
Number of Solutions of a Linear
System
Exactly One Solution
Infinitely Many Solutions
No Solution
Tell how many solutions the linear
system has.
2x – y = 1
-4x + 2y = -2
Tell how many solutions the linear
system has.
x + 2y = 4
x + 2y = 1
Tell how many solutions the linear
system has.
x – 5y = 5
x + 5y = 5
Basketball
Christie played in a basketball game in which she
scored a total of 21 points. In the game, she
made twice as many two-point shots as threepoint shots. How many of each type of shot did
Christie make?