How to Convert Equations with Variables?

In summary, solving a system of equations problem involves finding the values of all the variables that satisfy the given equations, and can be done using methods such as substitution, elimination, and graphing. The purpose of solving such a problem is to find solutions to real-world problems, analyze relationships between variables, and make predictions. A system of equations can have more than one solution, which can be infinite or non-existent. A consistent system has at least one solution, while an inconsistent system has none. A system of equations can have any number of variables, but the number of equations must equal the number of variables for a unique solution.
  • #1
smashbrohamme
97
1

Homework Statement


4/x - 3/y=0
6/x +3/2y = 2


so I can make my own variables up.

U= 4/x
V= 3/y

my problem is, how do I convert that on the second equation

would 6/x turn into 1.5U and 3/2y turn into 1/V?
 
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  • #2
smashbrohamme said:
would 6/x turn into 1.5U and 3/2y turn into 1/V?
No,
[tex]\frac{3}{2y} = 0.5V[/tex]

Or do you mean
[tex]\frac{3}{2}y[/tex]
?

You need to be precise!
 
  • #3
no i mean 3/2y meaning, the 2 and the y will be multiplied.
 

FAQ: How to Convert Equations with Variables?

1. How do you solve a system of equations problem?

Solving a system of equations problem involves finding the values of all the variables that satisfy all the given equations. This can be done by using different methods such as substitution, elimination, and graphing.

2. What is the purpose of solving a system of equations problem?

The purpose of solving a system of equations problem is to find the values of the variables that make all the given equations true. This can help in finding solutions to real-world problems, analyzing relationships between different variables, and making predictions.

3. Can a system of equations have more than one solution?

Yes, a system of equations can have more than one solution. This is known as an infinite solution, where the equations form the same line or are parallel to each other. It can also have no solutions, where the equations form parallel lines that never intersect.

4. What is the difference between a consistent and an inconsistent system of equations?

A consistent system of equations has at least one solution, while an inconsistent system of equations has no solution. This can be determined by graphing the equations or using algebraic methods, such as substitution or elimination.

5. Can a system of equations problem have more than two variables?

Yes, a system of equations problem can have any number of variables. However, the number of equations must be equal to the number of variables to have a unique solution. If the number of equations is less than the number of variables, the system will have an infinite number of solutions.

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