Math16 Case

1) The system have ALL REAL SOLUTIONS, when the final step you got TRUE statement like this:

2x+3y =6

4x+6y =12

Solve this system. What is the solution of the system?

We see if I times 2 both sides of first equation --> it become

4x+6y+12, so now i subtract this from second equation, I got

4x-4x +6y-6y = 12-12

0=0. TRUE STATEMENT. This is ALWAYS TRUE FOR ANY VALUE of X and Y. So we conclude: ALL REAL NUMBERS.

2) For no real solution, when final step we get FALSE STATEMENT

2x+4y=6

4x -8 = -8y find solution?

Solve second equation : we have

4x -8 = -8y

4x +8y = 8 ( add 8 and add 8y both sides)

Now times 2 both sides for first equation, I have

4x+8y = 12

We have a new system :

4x+8y = 12

4x +8y = 8

Now subtract both sides

4x-4x+8y-8y = 12-8 =4

0=4 is a FALSE STATEMENT.

So, FALSE STATEMENT, we conclude the system: NO REAL SOLUTION.

Week 4 Concept Check

On a Cartesian graph, x = 4 is a vertical line because the slope of the line is undefined. The slope of a line is "the change in y divided by the change in x." Since x never changes, the formula for finding the slope results in a division by zero. All lines with an undefined slope are vertical lines.

Week 6 concept check

After putting the equations of two lines into the y = mx + b equation, the m represents the slopes of the lines. To determine if two lines are perpendicular, multiply their m values, or slopes, together and look at the product. If the product is anything else but

-1, the lines are not perpendicular.

Week 8 concept check

The graph of the interval [-4,10] is a horizontal line with its left endpoint at -4 and its right endpoint at 10.

The "[" indicates that -4 is included in the interval; we represent this by drawing a heavy dot at the left endpoint -4.

The "]" indicates that 10 is included in the interval; we represent this by drawing a heavy dot at the right