Download 3.1 – Solve Linear Systems by Graphing

3.1 – Solve Linear Systems by
Graphing
A system of two linear equations in two
variables x and y, also called a linear system,
consists of two equations that can be written
in the following form.
Ax + By = C
Dx + Ey = F
A solution of a system of linear equations in
two variables is an ordered pair that satisfies
each equation.
3.1 – Solve Linear Systems by
Graphing
Example 4:
Graph the linear system and estimate the solution. Then
check the solution algebraically.
3x + 2y = -4
x + 3y = 1
3.1 – Solve Linear Systems by
Graphing
Example 5:
Graph the linear system and estimate the solution. Then
check the solution algebraically.
4x – 5y = -10
2x – 7y = 4
3.1 – Solve Linear Systems by
Graphing
A system that has at least one solution is
consistent. If a system has no solution, the
system is inconsistent.
A consistent system that has exactly one
solution is independent and a consistent
system that has infinitely many solutions is
dependent.
3.1 – Solve Linear Systems by
Graphing
3.1 – Solve Linear Systems by
Graphing
Example 6:
Solve the system. Then classify the system as consistent and
independent, consistent and dependent, or inconsistent.
4x – 3y = 8
8x – 8y = 16
3.1 – Solve Linear Systems by
Graphing
Example 7:
Solve the system. Then classify the system as consistent and
independent, consistent and dependent, or inconsistent.
2x + y = 4
2x + y = 1