Find System of 2 Equations in 2 Vars for x=t, y=3t-4

In summary, the given parametric representation of x=t and y=3t-4 does not satisfy the requirements for a system of two equations in two variables. It is likely a mistake in the problem and a second equation would need to be added to have a unique solution.
  • #1
bbdynamite
3
0

Homework Statement


Find a system of two equations in two variables, x and y, that has the solution set given by the parametric representation x=t and y=3t-4, where t is any real number.


Homework Equations


x=t and y=3t-4, where t is any real number


The Attempt at a Solution


y=3x-4 which means that x=(y+4)*1/3. But that is still only one equation and I can't figure out what the other one is. If there are two equations with two unknowns, couldn't the solutions be precise numbers? Since the solution given is parametric, I think there is only one equation in two variables. However, this does not satisfy the question's requirements. What is going on?
 
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  • #2
bbdynamite said:

Homework Statement


Find a system of two equations in two variables, x and y, that has the solution set given by the parametric representation x=t and y=3t-4, where t is any real number.

Homework Equations


x=t and y=3t-4, where t is any real number

The Attempt at a Solution


y=3x-4 which means that x=(y+4)*1/3. But that is still only one equation and I can't figure out what the other one is. If there are two equations with two unknowns, couldn't the solutions be precise numbers? Since the solution given is parametric, I think there is only one equation in two variables. However, this does not satisfy the question's requirements. What is going on?

I agree with you. It's probably just a mistake in the problem. If you want a second equation you could always suggest something like x=x or something else redundant. But that's pretty pointless.
 
  • #3
OK thanks for confirming my thought.
 
  • #4
Two independent equations in x and y will necessarily have a unique solution, not an infinite set of equations as you are given. Yes, x and y must satisfy y= 3x- 4 which I would write as 3x- y= 4. A second equation must be a multiple of that, say, 9x- 3y= 12.
 

FAQ: Find System of 2 Equations in 2 Vars for x=t, y=3t-4

What is a system of equations?

A system of equations is a set of two or more equations that contain multiple variables and can be solved simultaneously to find a solution that satisfies all the equations.

How many variables are in a system of 2 equations in 2 variables?

A system of 2 equations in 2 variables will have 2 variables, typically represented as x and y.

How do you solve a system of equations?

To solve a system of equations, you can use different methods such as substitution, elimination, or graphing. The goal is to find values for the variables that will make both equations true.

What is the solution to the system of equations x=t, y=3t-4?

The solution to this system of equations is (t, 3t-4), where t is any real number. This means that for any value of t, the values of x and y that satisfy both equations are (t, 3t-4).

Can a system of equations have more than one solution?

Yes, a system of equations can have more than one solution. In fact, there can be infinitely many solutions if the equations are dependent (meaning they represent the same line) or if the equations are inconsistent (meaning they have no solution).

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