When two lines cross at one point
What is Consistent and Independent
How many solutions does the equation
2(x+10)-17=5+2x-2
have?
Infinite
In solving by graphing, how many lines do you need to graph?
At least two.
What are the dimensions of this matrix
4 -3
0 1
5 6
3x2
This is where you plot points of two lines to see where the two lines cross.
What is Solving by Graphing.
Solve by substitution
3x-6y=9
-4x+7y=-16
X=11
Y= 4
When graphed, if two lines are directly on top of each other, how many solutions is there?
Infinite
Consistent and Dependent
What are the elements of a Matrix
The numbers in the matrix
Rows and Columns
When two lines have the same slope and y-intercept
What is Consistent and Dependent
The same line
When graphing an equation in y=mx+b form, what is the first step?
Identify the slope and y-intercept
Is (4,1) a solution of: x + 2y = 6, x - y = 3
Yes, (4) + 2(1) = 6 (4) - (1) = 3
Solve
2 1 + 4 6
0 -3 -2 -1
6 7
-2 -4
When two lines have the same slopes but different y-intercepts
Inconsistent
Solve by elimination
6x+15y=-12
-2x-5y=9
0=15
No Solution
If the slopes are the same and the y-intercepts are different, how many solutions does the system have?
No Solution
Solve
2 1
0 3 + 4 3 0
2 1 -1 3 6
Not the same dimension
No Solution
What is system of linear equations ?
Two or more equations
find all values of x and y that satisfies both inequalities
2x-(1/2)y > 4
4x-y<5
Inconsistent
Is (1,3) a solution of: 2x + y = 5, -2x + y = 4
No, 2(1) + (3) = 5 but -2(1) + 3 = 1, not 4
Use a matrix to solve this system of linear equation
4x+5y+3z= 15
x-3y+2z= -6
-x+2y-z= 3
X= 2
Y= 2
Z= -1