SOLUTION: Solve the system using any method. (Simplify your answer completely. If the system is dependent, enter a general solution in terms of x and y. If there is no solution, enter NO SOL

Algebra ->  Coordinate Systems and Linear Equations  -> Lessons -> SOLUTION: Solve the system using any method. (Simplify your answer completely. If the system is dependent, enter a general solution in terms of x and y. If there is no solution, enter NO SOL      Log On


   

Question 1130652: Solve the system using any method. (Simplify your answer completely. If the system is dependent, enter a general solution in terms of x and y. If there is no solution, enter NO SOLUTION.)
5x − 2y = 22
y= 5/2 x - 11
Found 3 solutions by MathLover1, ikleyn, MathTherapy:
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

5x+-+2y+=+22
y=+%285%2F2%29+x-11
--------------------
5x+-+2y+=+22
-%285%2F2%29+x%2By=+-11
Solved by pluggable solver: Solving a System of Linear Equations by Elimination/Addition


%28-5%2F2%29%2Ax%2B%281%29%2Ay=-11 Start with the second equation


2%28%28-5%2F2%29%2Ax%2B%281%29%2Ay%29=%282%29%2A%28-11%29 Multiply both sides by the LCD 2



-5%2Ax%2B2%2Ay=-22 Distribute and simplify



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Lets start with the given system of linear equations

5%2Ax-2%2Ay=22
-5%2Ax%2B2%2Ay=-22

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 5 and -5 to some equal number, we could try to get them to the LCM.

Since the LCM of 5 and -5 is -5, 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%285%2Ax-2%2Ay%29=%2822%29%2A-1 Multiply the top equation (both sides) by -1
-1%2A%28-5%2Ax%2B2%2Ay%29=%28-22%29%2A-1 Multiply the bottom equation (both sides) by -1


So after multiplying we get this:
-5%2Ax%2B2%2Ay=-22
5%2Ax-2%2Ay=22

Notice how -5 and 5 add to zero, 2 and -2 add to zero, -22 and 22 and to zero (ie -5%2B5=0) 2%2B-2=0, and -22%2B22=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(52788) 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.



Answer by MathTherapy(10552) About Me  (Show Source):
You can put this solution on YOUR website!

Solve the system using any method. (Simplify your answer completely. If the system is dependent, enter a general solution in terms of x and y. If there is no solution, enter NO SOLUTION.)
5x − 2y = 22
y= 5/2 x - 11
That woman's answer is WRONG!

She uses the most time-consuming and INEFFICIENT way to solve a system yet she comes up with an INCORRECT answer!





2y = 5x - 22 ------ Multiplying eq (ii) by 2

- 5x + 2y = - 22 ------- eq (iii)

Adding eqs (iii) & (i) gives us: 0 = 0.

The system has an INFINITE NUMBER of SOLUTIONS, hence it's DEPENDENT!