Solving Linear Equations: Inconsistent, Dependent & Independent

In summary, the conversation is about solving systems of linear equations and whether or not they need to be in slope intercept form. The person asking for help is unsure how to get the equations into that form and is seeking an explanation. The summarizer points out that it is not necessary to have the equations in slope intercept form to solve the problem and provides a solution for the first system of equations. The person asking for help clarifies that they need the equations in slope intercept form, but the summarizer questions why that is necessary for the original problem.
  • #1
torid
2
0
solve each system of linear equations. Indicate whether each system is inconsistant, dependent, or independent.

i'm not sure how to get these problems into slope intercept form: y=mx+b

1.
3x - 6y=9
1/2x=y +3/2

2.
2x + 3y=1
-3x + 4y=-10

3.
0.5x - 0.75y=0.125
4x-6y=12

if anyone could explain to me how to do these problems, that would be great.
i just don't understand how to get them into slope.
but i do get how to graph them.
 
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  • #2
You don't get them into slope-intercept form. You just solve them or show you can't. Solve one equation, for example, for x and substitute that expression into the other equation.
 
  • #3
yeah. but i do need them in slope intercept form, so maybe you could explain how i get them there.
 
  • #4
torid said:
yeah. but i do need them in slope intercept form, so maybe you could explain how i get them there.

No, you don't get need them in slope intercept form. I'll give you a big hint, the solution to the first one is x=6, y=3/2. That's a single point. You don't express that in slope intercept form. It's a POINT. Now, how did I get that solution?
 
  • #5
Please explain why you need to get them in slope intercept form? If the problem requires you to do that, why didn't you say so in your first post? You said the problem was to "Indicate whether each system is inconsistant, dependent, or independent"! That has little to do with "slope intercept" form. And, I should point out that "problem" don't have a slope intercept form so it is unclear what you mean by "get these problems into slope intercept form"!

If you mean get each equation into slope intercept form (again, not necessary for doing what you first said you wanted to do nor even a good idea), you say, correctly, that slope intercept form is "y= mx+ b". Do you notice the "y" alone on the left side? Solve each equation for y. If you know what slope intercept form is, or are working on systems of equations, you certainly should know how to solve a single linear equation.
 

Related to Solving Linear Equations: Inconsistent, Dependent & Independent

What is a linear equation?

A linear equation is an algebraic equation in which each term is either a constant or the product of a constant and a single variable. It can be written in the form y = mx + b, where m is the slope and b is the y-intercept.

What is the difference between inconsistent, dependent, and independent linear equations?

An inconsistent linear equation has no solution, meaning that there is no value for the variable that will make the equation true. A dependent linear equation has infinitely many solutions, meaning that any value for the variable will make the equation true. An independent linear equation has exactly one solution, meaning that there is only one value for the variable that will make the equation true.

How do you solve a linear equation?

To solve a linear equation, you must isolate the variable on one side of the equation by using inverse operations. This means that whatever operation is being done to the variable, you must do the opposite operation to both sides of the equation in order to cancel it out. Repeat this process until the variable is by itself on one side of the equation.

How do you know if a linear equation is inconsistent, dependent, or independent?

An inconsistent linear equation will result in a statement that is always false, such as 0 = 5. A dependent linear equation will result in a statement that is always true, such as 3 = 3. An independent linear equation will result in a statement that is only true for one specific value, such as 2 = 2.

What are some real-life applications of solving linear equations?

Linear equations are used in many real-life situations, such as calculating a car's fuel efficiency, determining the cost of a phone plan, or figuring out how much a company will make in profits based on their sales. They are also used in engineering and physics to solve problems involving speed, distance, and time.

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