10 - 11 Systems of Equation & Inequalities Flashcards

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1
Q

define

a system of equations refers to

A

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

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2
Q

technique

what are two ways to solve systems of 2 equations?

A

substitution & elimination

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3
Q

confusing concept

when does a system of equations have no solutions?

A

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

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4
Q

confusing concept

when does a system of equations have infinite solutions?

A

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

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5
Q

technique

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

A

substitution

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6
Q

technique/confusing concept

what are the solutions to a system of equations?

A

the intersection points of the graphs of the equations

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7
Q

confusing concept

if there is only one intersection point,

A

there is only one solution

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8
Q

confusing concept

if the lines are parallel,

A

they have no intersection points; they have the same slope

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9
Q

confusing concept

if two lines are the same,

A

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

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10
Q

technique

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

A

solve the system consisting of equations

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11
Q

confusing concept

only reverse the sign of the inequality when

A

you multiply or divide both sides by a negative number

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12
Q

confusing concept

y > -x-1 represents all the points

A

ABOVE the line y = -x-1

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13
Q

confusing concept

in the graph y ≥ -x-1, the line is

A

solid and points on the line would satisfy the inequality

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14
Q

technique

what is the goal when it comes to graphing?

A

to find the region with the points that satisfy the system

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15
Q

example

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

A

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

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16
Q

example

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

A
  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)