10 - 11 Systems of Equation & Inequalities

Question 1

define

a system of equations refers to

Answer 1

2 or more equations that deal with the same set of variables

Question 2

technique

what are two ways to solve systems of 2 equations?

Answer 2

substitution & elimination

Question 3

confusing concept

when does a system of equations have no solutions?

Answer 3

when the same equation is set to a different constant
ex. 3x + 2y = 5
3x + 2y = -4
ex. 3x + 2y = 5
6x + 4y = -8

Question 4

confusing concept

when does a system of equations have infinite solutions?

Answer 4

when both equations are essentially the same
ex. 3x + 2y = 5
3x + 2y = 5
ex. 3x + 2y = 5
6x + 4y = 10

Question 5

technique

what do you use in complex systems?
e.g.
y + 3x = 0
x^2 + 2y^2 = 76

Answer 5

substitution

Question 6

technique/confusing concept

what are the solutions to a system of equations?

Answer 6

the intersection points of the graphs of the equations

Question 7

confusing concept

if there is only one intersection point,

Answer 7

there is only one solution

Question 8

confusing concept

if the lines are parallel,

Answer 8

they have no intersection points; they have the same slope

Question 9

confusing concept

if two lines are the same,

Answer 9

they overlap and intersect in an infinite number of places; hence an infinite number of solutions

Question 10

technique

to find the point(s) where two graphs intersect,

Answer 10

solve the system consisting of equations

Question 11

confusing concept

only reverse the sign of the inequality when

Answer 11

you multiply or divide both sides by a negative number

Question 12

confusing concept

y > -x-1 represents all the points

Answer 12

ABOVE the line y = -x-1

Question 13

confusing concept

in the graph y ≥ -x-1, the line is

Answer 13

solid and points on the line would satisfy the inequality

Question 14

technique

what is the goal when it comes to graphing?

Answer 14

to find the region with the points that satisfy the system

Question 15

example

how many solutions do these systems of equations have:
2y - 4x = 2
y = 2x = 1

Answer 15

infinite solutions
it’s just one line–they’re the same line

Question 16

example

where do the two graphs intersect?
y = 3x - 5
y = -2x + 10

Answer 16

1. substitute the first equation with the second
   3x - 5 = -2x + 10
   5x = 15
   x = 3
2. substitue when x = 3,
   y = 3(3) - 5 = 4
   –> the two lines intersect at (3,4)