What is the solution?
What does the solution to a system of equation represents?
The solution is the point where both equations are true at the same time.
Two line have the same slope but different y-intercepts. How many solutions
No solution, the lines are parallel
When is graphing a good method to use?
Graphing is good when equations are already in slope intercept form (Y=mx+b) and the intersection is clear.
Solve by inspection:
y=x+2
y=x-1
How many solutions?
Same slope + Different Y-intercept= No solution.
What does the intersection mean in a real world situation?
The intersection represents a situation where both conditions are met at the same time.
Why is the solution written as an order pair (x,y)?
Because a solution gives both an x value and y value that work.
Two equations simplify to the same equation. How many solutions?
Infinite Solutions, same line
When is elimination the most efficient strategy?
Elimination work best when variables can be easily eliminated by adding or subtracting.
solve:
y=3
y=-2x+3
(0,3)
Why do real world system solution usually need context to make sense?
Because numbers must make sense in context ( no negative time, distance, etc. )
What does it mean if two lines intersect at exactly one point?
The system has one solution because the lines intersect once's.
Why do parallel lines have no solution?
The never intersect each other, so there is no point that satisfies both equations.
When does substitution make the most sense?
Substitution works best when one equation is already solved for a variable.
Solve using elimination:
x+y=6
x-y=2
(4,2)
Give an example of a real world situation that could be model by a system.
EX; Two people saving money at different rates and ending with the same amount.
What does it mean if two lines never intersect?
The system has no solution because the never intersect each other.
How can you tell without graphing that a system of equation has no solutions?
If the slopes are the same but the Y-intercept are different, the system has no solution.
Why might one method be easier than other for the same system?
Some method require fewer steps or less rewriting, making them more efficient.
Without solving, Predict the number of solutions:
y=2x+1
2y=4x+2
Infinitely many solutions.
Why might a system of equation have no solution in real life?
If conditions can't happen at the same time ( like different costs that never match), there is no solutions.
Explain what it means when two equations have infinitely many solutions?
The equation represent the same line (the lines are overlapping), so there are infinitely many solutions.
Explain how slope and Y-intercept help you predict the number of solutions.
Same slope + same Y-intercept = Infinitely solutions.
Same slope + different Y-intercept= No solution
Different slopes = One solution.
Given a system of equation, explain how you would choose a strategy before solving?
Looking at the equation first, then choosing the method that requires less work (not random).
Solve:
3x+2y=10
6x+4y=20
Infinite solution
Explain how checking the solution helps you avoid mistakes on word problems.
Checking ensures the order pair works in both equations, preventing careless mistakes.