Download Write Equation

Special Types of
Linear Systems
February 6, 2014
Pages 459-462
7.5 SPECIAL TYPES OF LINEAR
SYSTEMS
Students will be able to:
 Solve
special systems of linear
equations in two variables.
 Classify
systems of linear equations
and determine the number of
solutions.
Without solving the linear system, tell whether the
linear system has one solution, no solution, or
infinitely many solutions.
1.
5x + y = – 2
Equation 1
–10x – 2y = 4
Equation 2
SOLUTION
y = – 5x – 2
Write Equation 1 in slopeintercept form.
y = – 5x – 2
Write Equation 2 in slopeintercept form.
ANSWER
Because the lines have the same slope and the same
y-intercepts, they are the same line and there are
infinitely many solutions.
2.
6x + 2 y = 3
6x + 2 y = – 5
Equation 1
Equation 2
SOLUTION
3
2
Write Equation 1 in slope- intercept form.
y = – 3x – 5
2
Write Equation 2 in slope-intercept form.
y = – 3x +
ANSWER
Because the lines have the same slope but different yintercepts, the lines are parallel and the system has no
solution.
3.
x – 3y = – 15
2x – 3y = – 18
SOLUTION
y=1x+5
3
y=2x+6
3
Equation 1
Equation 2
Write Equation 1 in slopeintercept form.
Write Equation 2 in slopeintercept form.
ANSWER
Because the lines have different slope and different
y-intercepts,the system has one solution.
HOMEWORK
Worksheet