Pictures
Points of intersections of two lines.
What is the graphical solution to a system of equations?
We use this when we see opposites between 2 equations of two variables.
What is the addition method?
Rewriting a variable in one equation using information from the other.
What is the substitution method?
What are the 3 ways we can solve systems of equations?
0, 1, or infinitely many.
How many solutions a system of equations can have?
We use this when we notice similarities between 2 equations of 2 variables.
What is the subtraction method?
(Weight1)(Distance1)=(Weight2)(Distance2)
What is the Moment-Balance Equation?
Figuring out how to combine 2 or more things to get a precise percentage.
What is a mixture problem?
The equations create the same line twice.
What are repeated equations?
Multiply an equation to force in a similarity/difference.
What if there isn't a similarity or difference?
Solve one of the equations for 'y=...' or 'x=...'
What is the first step of the substitution method?
A collection of points that satisfy an equation.
What is a graph?
What are parallel lines?
A new line that shares a point of intersection with 2 other lines.
What is the graph of 2 added/subtracted equations?
What is the substitution method?
It is the solution to the system:
y=3-x
2x+4y=2
What is the point (5,-2)
Reduce the number of variables.
What is the goal when working with a system of equations?
Would be inconsistent with the equation:
y=-3/4xWhat is a graph with slope -3/4 and nonzero y-intercept?
It is a solution to the system:
-4x+y=-8
5x-3y=3
What is (3,4)?
The methods end up with an equations that is never true.