10 - 11 Systems of Equation & Inequalities Flashcards
define
a system of equations refers to
2 or more equations that deal with the same set of variables
technique
what are two ways to solve systems of 2 equations?
substitution & elimination
confusing concept
when does a system of equations have no solutions?
when the same equation is set to a different constant
ex. 3x + 2y = 5
3x + 2y = -4
ex. 3x + 2y = 5
6x + 4y = -8
confusing concept
when does a system of equations have infinite solutions?
when both equations are essentially the same
ex. 3x + 2y = 5
3x + 2y = 5
ex. 3x + 2y = 5
6x + 4y = 10
technique
what do you use in complex systems?
e.g.
y + 3x = 0
x^2 + 2y^2 = 76
substitution
technique/confusing concept
what are the solutions to a system of equations?
the intersection points of the graphs of the equations
confusing concept
if there is only one intersection point,
there is only one solution
confusing concept
if the lines are parallel,
they have no intersection points; they have the same slope
confusing concept
if two lines are the same,
they overlap and intersect in an infinite number of places; hence an infinite number of solutions
technique
to find the point(s) where two graphs intersect,
solve the system consisting of equations
confusing concept
only reverse the sign of the inequality when
you multiply or divide both sides by a negative number
confusing concept
y > -x-1 represents all the points
ABOVE the line y = -x-1
confusing concept
in the graph y ≥ -x-1, the line is
solid and points on the line would satisfy the inequality
technique
what is the goal when it comes to graphing?
to find the region with the points that satisfy the system
example
how many solutions do these systems of equations have:
2y - 4x = 2
y = 2x = 1
infinite solutions
it’s just one line–they’re the same line