SOLUTION: Use elimination to solve the system. (Simplify your answer completely. If the system is dependent, enter a general solution in terms of x and y.) x − y = 9 1/3 x = 1/3 y

Algebra ->  Coordinate Systems and Linear Equations  -> Lessons -> SOLUTION: Use elimination to solve the system. (Simplify your answer completely. If the system is dependent, enter a general solution in terms of x and y.) x − y = 9 1/3 x = 1/3 y       Log On


   

Question 1130654: Use elimination to solve the system. (Simplify your answer completely. If the system is dependent, enter a general solution in terms of x and y.)
x − y = 9
1/3 x = 1/3 y + 3
Found 2 solutions by MathLover1, ikleyn:
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

x+-y+=+9
%281%2F3%29+x+=+%281%2F3%29+y+%2B+3
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x+-y+=+9
%281%2F3%29+x+-%281%2F3%29+y=+3

Solved by pluggable solver: Solving a System of Linear Equations by Elimination/Addition


%281%2F3%29%2Ax%2B%28-1%2F3%29%2Ay=3 Start with the second equation


3%28%281%2F3%29%2Ax%2B%28-1%2F3%29%2Ay%29=%283%29%2A%283%29 Multiply both sides by the LCD 3



1%2Ax%2B-1%2Ay=9 Distribute and simplify



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Lets start with the given system of linear equations

1%2Ax-1%2Ay=9
1%2Ax-1%2Ay=9

In order to solve for one variable, we must eliminate the other variable. So if we wanted to solve for y, we would have to eliminate x (or vice versa).

So lets eliminate x. In order to do that, we need to have both x coefficients that are equal but have opposite signs (for instance 2 and -2 are equal but have opposite signs). This way they will add to zero.

So to make the x coefficients equal but opposite, we need to multiply both x coefficients by some number to get them to an equal number. So if we wanted to get 1 and 1 to some equal number, we could try to get them to the LCM.

Since the LCM of 1 and 1 is 1, we need to multiply both sides of the top equation by 1 and multiply both sides of the bottom equation by -1 like this:

1%2A%281%2Ax-1%2Ay%29=%289%29%2A1 Multiply the top equation (both sides) by 1
-1%2A%281%2Ax-1%2Ay%29=%289%29%2A-1 Multiply the bottom equation (both sides) by -1


So after multiplying we get this:
1%2Ax-1%2Ay=9
-1%2Ax%2B1%2Ay=-9

Notice how 1 and -1 add to zero, -1 and 1 add to zero, 9 and -9 and to zero (ie 1%2B-1=0) -1%2B1=0, and 9%2B-9=0)


So we're left with

0=0


which means any x or y value will satisfy the system of equations. So there are an infinite number of solutions


So this system is dependent

Answer by ikleyn(52786) About Me  (Show Source):
You can put this solution on YOUR website!
.

The solution and the answer by @MathLover1 is   W R O N G.

The correct answer is :   The system is dependent.


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I am very surprised on how the tutor @LoverMath1 treats these problems on solving equation systems.

By applying this "pluggable solver", she turns / transforms / converts very serious educational task of teaching students
into some unreadable and nonsensical text.