Without graphing, is each system independent, dependent, or inconsistent? { -x-3y=0 x-y=4

2 answers:

6 0

First, determine if there is a solution to the equation by finding their intersection. If we are to rewrite the system of linear equations,

-x - 3y = 0
x - y = 4

The values of x and y from the equation are 3 and -1. The slopes of the equations, m, are also not the same as shown below,
m = -A/B

where A and B are the numerical coefficients of x and y, respectively.
m1 = -(-1/-3) = -1/3
m2 = -(1/-4) = 1/4

Hence, the equations are <em>independent.</em>

Kryger [21]3 years ago

5 0

Since we can find a solution for this system of equations we can affirm this is an independent system with solution equal to (x,y) = (3,-1)

* If we graph a dependent system in the slope - intercept form, we can see that the graphs of each one are identical to each (beacuse we are representing the same line).

*An inconsistent system occurs when the equations have the same slope, but different values of intersection with the Y axis.

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What is a number in which the digit 2 is one tenth the value of the digit 2 in 8.524?

Mashcka [7]

It is tens. 524
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4 0

4 years ago

A mine worker is in a tunnel 25 feet below the ground. He descends another 13 feet. What is his final position? i already know t

Marina86 [1]

Answer: -25 - 13

This simplifies to -38

So the worker's final position is 38 feet below the ground.

A diagram is shown below.

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Explanation:

Draw a vertical number line. Plot 0 on it to indicate the ground level, or surface level. Then plot -25 on it, which is below 0. This is 25 feet below the ground.

To move 13 further feet downward, we will subtract 13 from -25. Subtracting a positive means we move downward.

For example, start at the 30th of a building. This is marked as +30 or just 30 on the vertical number line. Subtract off 13 to go down 13 floors and we have 30-13 = 17. So after going down 13 floors, we're at the 17th floor now.

Going back to the problem at hand, we start at -25 and subtract off 13 to get the final answer -25 - 13

The answer is not -25 - -13 and it is not -25 - (-13). This is because the two negatives cancel to be a positive. So -25 - (-13) becomes -25+13. Here we're starting at -25 but then going up 13 feet. Instead we want to go down 13 feet.

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After we determine the expression is -25 - 13 we will effectively add the positive versions of those numbers like so

25+13 = 38

But the final answer is negative because we're starting underground and moving further underground.

We can write it like this

-25 - 13 = -(25+13) = -(38) = -38

Therefore, if the worker starts off 25 feet underground, and moves 13 feet downward, then the worker ends up 38 feet underground. Again, use the vertical number line to help see this.

Check out the diagram below.