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

[bbdynamite]

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?

 

[Dick]

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.

 

[bbdynamite]

OK thanks for confirming my thought.

 

[HallsofIvy]

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.