Transcript system of linear equations

Fredric wants to put a total of at least x stamps in 3 albums. If
he puts 44 stamps in the first album and 45 stamps in the
second album, which inequality describes s, the number of
stamps he should put in the third album?
How can you show all the solutions of
the linear equation y = 2x – 3?
Graph the line, of course!
Each point on the line is a solution.
Use the graph to write three
different solutions of the equation
y = 2x – 3. Test each ordered pair
to make the equation true.
(0,-3), (1,-1), (2,1), (3,3), (4,5)
Two or more linear equations together
form a system of linear equations.
One way to solve a system of linear
equations is by graphing. Any point
common to all the lines is a solution
of the system. So, any ordered pair
that makes all the equations true is a
solution of the system.
Solve the system of linear equations by graphing.
y = 2x – 3
y=x–1
Graph both of the equations on
the same coordinate grid.
Find the point of intersection.
The lines intersect at (2,1), so (2,1)
is the solution of the system.
Check: See if (2,1) makes both equations true.
y = 2x – 3
y=x–1
1 = 2(2) – 3
1 = (2) – 1
1=4–3
1=1
1=1
Solve the system of linear equations by graphing.
y=x+5
y = -4x
Graph both of the equations on
the same coordinate grid.
Find the point of intersection.
The lines intersect at (-1,4), so
(-1,4) is the solution of the system.
Check: See if (-1,4) makes both equations true.
y=x+5
y = -4x
(4) = (-1) + 5
(4) = -4(-1)
4=4
4=4
A system of linear equations has no solution
when the graphs of the equations are parallel.
There are no points of intersection, so there is no
solution.
y = -x + 1
y = -x – 1
y=½x+3
y=½x-2
A system of linear equations has
-4y = 4 + x infinitely many solutions when the
1
x + y = -1 graphs of the equations are the same
4
line. All points on the line are solutions
to the system.
First, write each equation in slope-intercept form.
-4y = 4 + x
-4y
x+4
=
-4
-4
1
y=- x–1
4
1
x + y = -1
4
1
1
- x
- x
4
4
1
y=- x–1
4
Graph the equations on the same coordinate plane.
Since the graphs are the same line, the system has
infinitely many solutions.
PRACTICE:
Solve the system of linear equations by graphing.
y=x
y=x+6
PRACTICE:
Solve the system of linear equations by graphing.
2x + 2y = 1
1
y = -x +
2
2x + 2y = 1
-2x
-2x
2y = -2x + 1
2y -2x + 1
=
2
2
1
y = -x +
2
1
y = -x +
2
PRACTICE:
Solve the system of linear equations by graphing.
x=1
x = -2
PRACTICE:
Solve the system of linear equations by graphing.
y=x
y = 5x
PRACTICE:
Solve the system of linear equations by graphing.
2x + y = 3
x – 2y = 4
2x + y = 3
-2x
-2x
y = -2x + 3
x – 2y = 4
-x
-x
-2y = -x + 4
-2y -x + 4
=
-2
-2
1
y = x-2
2
PRACTICE:
Solve the system of linear equations by graphing.
3x – y = 5
y = 3x – 5
3x – y = 5
-3x
-3x
-y = -3x + 5
-1y -3x + 5
=
-1
-1
y = 3x – 5
y = 3x – 5