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Posted by Ashley on Thursday, January 18, 2007 at 6:51pm.

px+qy=r 2px-qy=2r find the solution.

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math - bobpursley, Thursday, January 18, 2007 at 7:09pm

There are five unknowns here: p, q, r, x, y

If p, x, q, and y are unknowns, then the equation is not solvable. If p, q, and r are constants, then add the two equations
px+ qy=r
px -qy=r

adding
2px=2r
x= r/p then solve for y, which has to be zero, or q is zero.

As it is, the equation systems cannot be solved.

To solve the given system of equations:

px + qy = r
2px - qy = 2r

Step 1: Simplify the equations.
Add both equations together to eliminate the term "qy":
(px + qy) + (2px - qy) = r + 2r
3px = 3r
Divide both sides by 3:
px = r

Step 2: Solve for the variables.
From the equation px = r, we can isolate x by dividing both sides by p:
x = r/p

Step 3: Determine the value of y.
Since we cannot determine the exact value of y from the given equations, there are a few possible scenarios:
a) If y is any real number, then the solution is not unique.
b) If q is 0, then y can be any real number and the solution is not unique.
c) If y is 0, then q can be any real number and the solution is not unique.

In conclusion, if p, q, and r are constants, the solution to the given system of equations is:
x = r/p
y can be any real number if q is 0 or y = 0 if q is any real number.