Can someone please help me???? (algebra)

lillybeth

lillybeth

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I have a problem with a homework question that simply states: -3=x-2y An inequality i guess, but how do I solve it, i have no experience whatsoever with inequalitys and my mom is confused too.:mad:
thanks!!!
 
It is an equation, since there is an equals sign, and more specifically, a linear equation in two variables, meaning it describes a line in a plane, the xy-plane.

Are you supposed to graph it?
 
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lillybeth said:
I have a problem with a homework question that simply states: -3=x-2y An inequality i guess, but how do I solve it, i have no experience whatsoever with inequalitys and my mom is confused too.:mad:
thanks!!!
Click to expand...
Lillybeth

One of the hardest things to learn in algebra is that letters stand for numbers, but the kinds of statements that are made about numbers are of different kinds.

Sometimes a letter stands for a specific number. Example 4x + 1 = 5x - 8, which is an equation that is true only if x = 9.

Sometimes letters stand for a whole class of numbers. Example a + b = b + a. This is an equation that is true for every possible pair of numbers.

Sometimes letters stand for members of a special set of numbers that have a certain kind of relationship with each other. Example C = 5 * (F -32) / 9. This equation is true for an infinite set of pairs of numbers, but it is false for almost all pairs of numbers.

The fact that different kinds of truths can be expressed algebraically makes it hard to be sure what kind of truth is expressed in any particular algebraic statement, but it also means that algebraic language can express an immense range of truths. The equation tha you are looking at does not have a unique answer and so cannot be solved in the sense tha you are thinking. What does the question ask you to do?
 
JeffM said:
Lillybeth

One of the hardest things to learn in algebra is that letters stand for numbers, but the kinds of statements that are made about numbers are of different kinds.

Sometimes a letter stands for a specific number. Example 4x + 1 = 5x - 8, which is an equation that is true only if x = 9.

Sometimes letters stand for a whole class of numbers. Example a + b = b + a. This is an equation that is true for every possible pair of numbers.

Sometimes letters stand for members of a special set of numbers that have a certain kind of relationship with each other. Example C = 5 * (F -32) / 9. This equation is true for an infinite set of pairs of numbers, but it is false for almost all pairs of numbers.

The fact that different kinds of truths can be expressed algebraically makes it hard to be sure what kind of truth is expressed in any particular algebraic statement, but it also means that algebraic language can express an immense range of truths. The equation tha you are looking at does not have a unique answer and so cannot be solved in the sense tha you are thinking. What does the question ask you to do?
Click to expand...

there is no question, it just asks what ityped above.

 
MarkFL said:
It is an equation, since there is an equals sign, and more specifically, a linear equation in two variables, meaning it describes a line in a plane, the xy-plane.

Are you supposed to graph it?
Click to expand...

I dont know if i am supposed to graph it, my homework didnt tell me. The subject is solving linear equations, so i guess im supposed to solve for the variables. Can i do that with two variables?
 
lillybeth said:
I dont know if i am supposed to graph it, my homework didnt tell me. The subject is solving linear equations, so i guess im supposed to solve for the variables. Can i do that with two variables?
Click to expand...
In general, a single equation in two unknowns cannot be solved in the sense that you are thinking.

A single equation in two variables defines a relationship between pairs of numbers that can be graphed.

In general, a solution for n unknowns requires n equations.
 
lillybeth said:
I dont know if i am supposed to graph it, my homework didnt tell me. The subject is solving linear equations, so i guess im supposed to solve for the variables. Can i do that with two variables?
Click to expand...

Unless this is a Diophantine equation (restricted to integer values) with a further restriction that you find the smallest such solution among the natural numbers (1,2), then you won't get a unique solution.

As stated, any point on the line described by the equation is a solution. We could write the solution set as:

\(\displaystyle (x,y)=\left(x,\dfrac{x+3}{2} \right)\)

You need another equation in order to determine a unique solution, corresponding geometrically to the point(s) where the two lines (or curves in the case of a non-linear system) intersect.

If you are supposed to solve for the variables, you will have to do so in terms of both, i.e:

\(\displaystyle x=2y-3\)

\(\displaystyle y=\dfrac{x+3}{2}\)
 
MarkFL said:
Unless this is a Diophantine equation (restricted to integer values) with a further restriction that you find the smallest such solution among the natural numbers (1,2), then you won't get a unique solution.

As stated, any point on the line described by the equation is a solution. We could write the solution set as:

\(\displaystyle (x,y)=\left(x,\dfrac{x+3}{2} \right)\)

You need another equation in order to determine a unique solution, corresponding geometrically to the point(s) where the two lines (or curves in the case of a non-linear system) intersect.

If you are supposed to solve for the variables, you will have to do so in terms of both, i.e:

\(\displaystyle x=2y-3\)

\(\displaystyle y=\dfrac{x+3}{2}\)
Click to expand...

thanks guys, i guess i should get this but i am so really confused. I'll ask my dad about it later too, maybe he can explain it better in front of me with a pencil and paper. You guys are just too smart for me... :) Thanks for trying, but i am a dunce. You did help though! Thanks. I will tell you once i figure it out. bye!
 
If you are given the above equation and told merely to "solve" then it is not you who are the dunce...it is whomever wrote that problem. ;)
 
However, it is not uncommon for math books to give a line of instructions, such as "graph these equations" or "solve for y", followed by a list of numbered problems, the point being to apply the instructions to each problem. Before we knock the writer of the text book, I would like to know if that wasn't the case.
 
HallsofIvy said:
However, it is not uncommon for math books to give a line of instructions, such as "graph these equations" or "solve for y", followed by a list of numbered problems, the point being to apply the instructions to each problem. Before we knock the writer of the text book, I would like to know if that wasn't the case.
Click to expand...

:-| I told you what by text book said!
 
Linear Equation

Your equation is called linear because the greatest exponent that it has is 1.
Your equation is a straight line on the xy-plane.
With just two points in the form (x,y), you can graph any linear equation.
It is called linear because it forms a straight line as a graph.
 
harpazo said:
Your equation is called linear because the greatest exponent that it has is 1.
Your equation is a straight line on the xy-plane.
With just two points in the form (x,y), you can graph any linear equation.
It is called linear because it forms a straight line as a graph.
Click to expand...
Oh. Thanks, and I like your Avatar! :D
 
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