Substitution/Elimination

Substitution

100

-x+2y=6

3x-2y=2

What is, (2,2)

200

4x+y=7

2x+5y=-1

What is, (2,-1)

300

3x+2y=-2

6x-y=6

What is, (2/3,-2)

400

2x+4y=-4

x-2y=10

What is,(4,-3)

500

4x+y=-1

8x+2y=-2

What is, infinitely many solutions.

Elimination

100

-3x+3y=3

3x+y=9

What is, (2,3)

200

-5x+12y=20

x-2y=-6

What is, (-16, -5)

300

3x+2y=1

4x+6y=7

What is, (-4/5,17/10)

400

5x+7y=-2

2x-7y=9

What is, (1,-1)

500

4x+6y=8

2x+3y=3

What is, no solution

Definition

100

Mathematical model of a system, based on the use of a linear operator.

What is, linear systems

200

Way to solve linear equations by replacing numbers/variable.

What is, Substitution method

300

Way to solve linear systems by getting rid of a number/variable.

What is, Elimination Method

400

Branch of mathematics that deals with general statements of relations, utilizing letters and other symbols to represent the equation

What is, Algebra

500

Branch of mathematics that deals with the deduction of the properties, measurement, and relationships of points, lines, angles and figures.

What is, Geometry

Any Method

100

5x+7y=-2

2x-7y=9

What is, (10,10)

200

4x+6y=8

2x+3y=3

What is, (17/7, 9/7)

300

3x-8y=0

-2x+5y=-2

What is, (16,6)

400

2x-5y=3

-4x+10y=-6

What is, Infinitely many solutions

500

5/4x+y=-9/2

x+3/2y=-12

What is, (6,-12)

Types of solution

100

y=3x-1
1+ y=3x

What is Infinite Solutions

They are the SAME Equation.

200

y=5x-3

y=5x+3

What is NO Solution.

SAME SLOPE but DIFFERENT y-intercept

lines will never cross

300

2x+3y=6

3x+2y=6

What is 1 solution.

2x +3y=6 --> y=-2/3x +2

3x+2y=6 --> y=-3/2 + 3

SLOPES are Different and Y-intercept is Different

400

y= 9x+4

18x + 2y = -2

What is 1 solution.

y=9x+4

18x+2y= -2 --> y= -9x - 1

500

y= 3x + 9

-6x + 2y = -30

What is NO Solution.

y=3x+9

-6x+2y=-30  --> y= 3x-15

SAME SLOPE but DIFFERENT y-intercept