1/14/11- Today in class we learned about systems of linear equations: the graphing method, substitution method, and the elimination method. Systems of 2 linear equations always have an infinite number of solutions, the solutions are ordered pairs, they usually share one solution(point of intersection), they can share no solution(parallel lines), and they can be the same line sharing many solutions. Substitution method: ex.Determine whether the given ordered pair is a solution of the system. (2,-3); x=2y+8 2x+y=1 you substitute: 2=x -3=y x=2y+8 2=2(-3)+8 and it = 2=2, which is true. 2x+y=1 (2)+(-3)=1 which = 1=1 which is true. Since both equations are true, the answer is yes.
today we learned the graphing methods of the systems of linear equations.
when there is a system of two linear equations, the graphs are lines, each line has an infinite # of solutions, which are ordered pairs. But the solution for both lines must satisfy both lines.
usually, the two equations share one solution, which is the point of intersection. Occasionally, the 2 equations/lines share NO solution, because they are parellel and don't itersect. But when the equations are the same line, they have infinitely many solutions.
to find the solutions, you can either use the three methods of solving linear equations-by table, by intercepts, or with slopes and intercepts- or you can solve by graphing.
SOLVE BY USING THEE 3 METHODS...
a) (2,-3); x=2y+8 2x+y=1 x=2y+8 2=2(-3)+8 substitute 2=-6+8 2=2 TRUE
2x+y=1 2(2)-3=1 substitute 4-3=1 1=1 TRUE
The ordered pair (2,-3) is a solution of the system.
Journal Entry January 14, 2011: Today, in Mr.Gersons Algebra 1 class, we learned all the systems of linear equations.They are graphing, substitution, and elimination method. We used those methods to solve the system of two linear equations. The following rules are always true: □Graphs are lines. ■Each solution has an ∞# of solutions. □Solutions are ordered pair. ■Solution must satisfy both equations.
These are the rules that can sometimes be true: □Usually share one solution. ■Point of intercept. □Can share no solutions. ■Parallel lines. □Can share ∞ many solutions. ■Same line. Now on to the example.
EXAMPLE: Determine wether the given ordered pair is a solution of the system.
a.) (2,-3); x=2y+8 2x+y=1 x=2y+8 (2)=2(-3)+8 Substitute 2=-6+8 2=2 First one is true, onto the second one. 2x+y=1 2(2)+(-3)=1 Substitute 4-3=1 1=1 Second one is also true which means that... The ordered pair given is a solution,TRUE.
I can't really show a whole graph on here, but I will show the part until graphing. EXAMPLE: Solve by graphing. x+y=2 x+y=6 x+y=2 -x -x Subtract x from both sides. y=-x+6 m=-1 y-intercept=6 Now the second equation. x-y=2 -x -x Subtract x from both sides. -y=-x+2 -1 -1 Divide -1 to both sides. y=x-2 m=1 y-intercept=-2 Then you graph this by using one of the three graphing linear equations. I usualyy use slope and intercept. Ryo Takatori Period 4 A(o3o)A Its still Friday~
7 comments:
This assignment is really easy!
Did we have homework On thursday too? Im sick in bed with a 103 fever >_<
1/14/11- Today in class we learned about systems of linear equations: the graphing method, substitution method, and the elimination method. Systems of 2 linear equations always have an infinite number of solutions, the solutions are ordered pairs, they usually share one solution(point of intersection), they can share no solution(parallel lines), and they can be the same line sharing many solutions. Substitution method: ex.Determine whether the given ordered pair is a solution of the system. (2,-3); x=2y+8 2x+y=1 you substitute: 2=x -3=y x=2y+8 2=2(-3)+8 and it = 2=2, which is true. 2x+y=1 (2)+(-3)=1 which = 1=1 which is true. Since both equations are true, the answer is yes.
Journal entry for 1/14-
today we learned the graphing methods of the systems of linear equations.
when there is a system of two linear equations, the graphs are lines, each line has an infinite # of solutions, which are ordered pairs. But the solution for both lines must satisfy both lines.
usually, the two equations share one solution, which is the point of intersection. Occasionally, the 2 equations/lines share NO solution, because they are parellel and don't itersect. But when the equations are the same line, they have infinitely many solutions.
to find the solutions, you can either use the three methods of solving linear equations-by table, by intercepts, or with slopes and intercepts- or you can solve by graphing.
SOLVE BY USING THEE 3 METHODS...
a) (2,-3); x=2y+8 2x+y=1
x=2y+8
2=2(-3)+8 substitute
2=-6+8
2=2
TRUE
2x+y=1
2(2)-3=1 substitute
4-3=1
1=1
TRUE
The ordered pair (2,-3) is a solution of the system.
***********************************
SOLVE BY GRAPHING
x-y=2 x+y=6
-x -x -x -x
-y=-x+2 y=-x+6
-1(-y)=-1(-x +2)
y=x-2
GRAPH TO DETERMINE THE POINT OF INTERSECTION, THE SOLUTION!!!
Moet Takata period 4
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Two people seriously?
@Jenna no we didn't have homework.
Journal Entry January 14, 2011:
Today, in Mr.Gersons Algebra 1 class, we learned all the systems of linear equations.They are graphing, substitution, and elimination method. We used those methods to solve the system of two linear equations. The following rules are always true:
□Graphs are lines.
■Each solution has an ∞# of solutions.
□Solutions are ordered pair.
■Solution must satisfy both equations.
These are the rules that can sometimes be true:
□Usually share one solution.
■Point of intercept.
□Can share no solutions.
■Parallel lines.
□Can share ∞ many solutions.
■Same line.
Now on to the example.
EXAMPLE:
Determine wether the given ordered pair is a solution of the system.
a.) (2,-3); x=2y+8 2x+y=1
x=2y+8
(2)=2(-3)+8 Substitute
2=-6+8
2=2
First one is true, onto the second one.
2x+y=1
2(2)+(-3)=1 Substitute
4-3=1
1=1
Second one is also true which means that...
The ordered pair given is a solution,TRUE.
I can't really show a whole graph on here, but I will show the part until graphing.
EXAMPLE:
Solve by graphing.
x+y=2 x+y=6
x+y=2
-x -x Subtract x from both sides.
y=-x+6 m=-1 y-intercept=6
Now the second equation.
x-y=2
-x -x Subtract x from both sides.
-y=-x+2
-1 -1 Divide -1 to both sides.
y=x-2 m=1 y-intercept=-2
Then you graph this by using one of the three graphing linear equations. I usualyy use slope and intercept.
Ryo Takatori Period 4
A(o3o)A
Its still Friday~
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