Solving Systems of Equations

Vocabulary

100

When two lines cross at one point

What is Consistent and Independent 

200

This is where you plot points of two lines to see where the two lines cross.

What is Solving by Graphing.

300

When two lines have the same slope and y-intercept

What is Consistent and Dependent 

The same line

400

When two lines have the same slopes but different y-intercepts

Inconsistent

500

What is system of linear equations ?

Two or more equations

Solving by Graphing

100

Solve by graphing: y = x - 3 y = -x - 1

solution is (1,-2)

200

Solve by graphing: y = -2x - 1 y = x + 5

Solution is ( -2,3)

300

Solve by graphing: y = 1/3x - 3, y = 4 - 2x

Solution is (3,-2)

400

Lawn Care charges $30 per bag of mulch and a $30 delivery fee. Yard Depot charges $25 per bag of mulch and $55 for a delivery fee. At what number of bags is the cost the same?

Solution is 5 bags, $180.

500

Anthony has $7 saved up and saves $1 more each week. Marc has $4 saved up and saves $2 more each week. When will they have the same amount saved up?

Solution is 3 weeks, $10

Random

100

How many solutions does the equation 

2(x+10)-17=5+2x-2 

have?

Infinite 

200

Solve by substitution

  3x-6y=9

-4x+7y=-16

X=11

Y= 4

300

When graphing an equation in y=mx+b form, what is the first step?

Identify the slope and y-intercept

400

Solve by elimination

  6x+15y=-12

  -2x-5y=9

0=15

No Solution

500

find all values of x and y that satisfies both inequalities

   2x-(1/2)y > 4

   4x-y<5

Inconsistent

Knowledge

100

In solving by graphing, how many lines do you need to graph?

At least two.

200

When graphed, if two lines are directly on top of each other, how many solutions is there?

Infinite

Consistent and Dependent

300

Is (4,1) a solution of: x + 2y = 6, x - y = 3

Yes, (4) + 2(1) = 6 (4) - (1) = 3

400

If the slopes are the same and the y-intercepts are different, how many solutions does the system have?

No Solution

500

Is (1,3) a solution of: 2x + y = 5, -2x + y = 4

No, 2(1) + (3) = 5 but -2(1) + 3 = 1, not 4

Matrix Operation

100

What are the dimensions of this matrix

 4  -3

 0    1

 5    6 

3x2

200

What are the elements of a Matrix

The numbers in the matrix

Rows and Columns

300

Solve 

2  1       +    4   6

0  -3           -2  -1

 6    7

-2  -4

400

Solve

2   1  

0   3     +   4   3   0

2   1          -1  3  6 

Not the same dimension

No Solution

500

Use a matrix to solve this system of linear equation

4x+5y+3z= 15

x-3y+2z= -6

-x+2y-z= 3

X= 2

Y= 2

Z= -1