Facts of Systems
How Many Solutions?
What is the Next Step?
100
How many equations are in a system of linear equations?
2 equations
100
What are the three possible solutions we have learned for a System of Linear Equations?
One solution, No solutions, Infinitely Many Solutions
100
What is the next step?
2x=4
Divide by 2 on each side
200
What is the goal when solving a System of Linear Equations?
To find one solution, no solution or infinitely many solutions
200
How many solutions are there in this System of Linear Equations?
1 solution
200
What is the next step?
3x-9=3
Add 9 to both sides
300
How can we tell that our equations are linear?
Straight lines
300
How many solutions are in this System of Linear Equations?
y=3x-8
y=3x+4
No Solutions
300
What is the next step?
3x+6+4x=-1
Combine the variable terms because they are like terms. (3x+4x)
400
How do we find the solution when there is one
Ordered pair or point where the two lines cross
400
How many solutions are in this System of Linear Equations?
y=-19x+8
y=19x+8
One Solution
400
What is the next step?
y=3x+4
y+2x=8
Substitute 3x+4 in for Y in the second equation
500
When you solve a One Solution System of Linear Equations, what should our answer look like?
(x, y)
ordered pair
500
Is this a type of solution to a linear equation?
No. It's not linear
500
What is the next step?
3x-8y=37
3x+6y=9
Subtract the equations to eliminate the X variable