Systems of Linear Equations

Name the solution

100

A system with two linear equations with the same slope and different y-intercepts are graphed what is there solution

No solution, they will never intersect.

200

A system of two linear equations that have the same slope and the same y-intercept are graphed, what is their solution?

Infinite solutions

300

A system of linear equations are graphed.  Two perpendicular lines are formed and intersect close to the origin.  How many solutions do they have? 

One solution

400

How many solutions does an inconsistent system have?

No solutions

500

How many solutions does a consistent system have

one if it is independent 

infinite if it is dependent

Name this formula

100

Y=mx + b is known as what form of equation?

Slope Intercept

200

Ax + By= C is known as what form of equation?

Standard

300

y-y1=m(x-x1) is known as what type of equation?

Point-Slope

400

What does rise/run represent?

y/x or the slope

500

what is the formula for slope?

m=(y-y1)/(x-x1)

Identify this method

100

y=2x +1

y=5x-1

The following lines are graphed to identify their point of intersection.  What method is being used to identify their solution?

Graphing

200

y=3x + 2

y= -x +6

(3x+2)= -x +6

What method is being used to solve this linear equation?

Substitution

300

2y-x=8

y+x=13

3y=21

y=7

What method was used to solve this system of equations?

Elimination using subtraction/addition

400

2y +3x =12

y +x=6

                       2y + 3x =12

-2(y+x=6).      -2y -2x=-12

What method is being used to solve this system of equations?

Elimination through multiplication

500

3x+6y=15

x+3y=9

(3x+6y=15) / -3.        -x-2y=-5

                                  x+3y= 9

                                   y=4

What method is being used to solve this system of equations?

Elimination using division

Solve this system

100

y=x-1

y=x-1

Infinite solutions, same line

200

y=2x-4

y=2x+4

Parallel lines, no solution

300

y=x-2

4+2y=2x

Infinite solutions, same line because

4+2y=2x = y=2x/2-4/2 or y=x-2

400

Solve using elimination

x+3y=9

x-2y=4

5y=5

y=1

x=6

500

Solve using substitution

y=3x+1

-2x+y=7

x=6

y=19

Substitution or Elimination?

100

y=2x+4

y=x-1

substitution

200

-y+x=3

y+3x=4

Elimination with subtraction/addition

300

y=9x+1

y=9x-1

No calculation needed, can tell that it is parallel and has no solution

400

y=x

2x=1/2 y+3

substitution because the y value is already set to x

500

x-3y=6

2x+y=3

Elimination using multiplication