How to calculate with two unknowns

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Discussion Overview

The discussion revolves around solving a system of two equations with two unknowns, specifically the equations \(4x-5y=7\) and \(3y-2x=1\). Participants explore methods for finding the values of \(x\) and \(y\) through algebraic manipulation.

Discussion Character

  • Mathematical reasoning
  • Homework-related
  • Technical explanation

Main Points Raised

  • One participant presents a method involving multiplying the second equation by 2 to facilitate elimination, leading to a solution for \(y\) and subsequently \(x\).
  • Another participant suggests a similar approach, emphasizing the addition of modified equations to find the values of the unknowns.
  • A comment is made regarding the use of "U" as an abbreviation for "you," which has a specific mathematical meaning, prompting a suggestion to use the full word instead.
  • A later reply acknowledges the suggestion and expresses intent to correct the usage of "U."

Areas of Agreement / Disagreement

Participants generally agree on the method of solving the equations through algebraic manipulation, though there is no consensus on the notation used in the discussion.

Contextual Notes

There are no explicit limitations or unresolved mathematical steps noted in the discussion.

Who May Find This Useful

This discussion may be useful for students learning to solve systems of equations, particularly those seeking different methods of approach and clarification on notation in mathematical writing.

headbang
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How to calculate with two unknowns.
Solve..

$$4x-5y=7$$
$$3y-2x=1$$
 
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headbang said:
How to calculate with two unknowns.
Solve..

$$4x-5y=7$$
$$3y-2x=1$$

$$ 4x-5y=7 \ \ (*)$$

We multiply both sides of the second equality by $2$, so we have:

$$2 \cdot (3y-2x)=2 \Rightarrow 6y-4x=2 \ \ (**)$$

$$(*)+(**) \Rightarrow 4x-5y+6y-4x=7+2 \Rightarrow y=9$$

$$4x-5y=7 \overset{y=9}{\Rightarrow } 4x-5 \cdot 9=7 \Rightarrow 4x-45=7 \Rightarrow 4x=52 \Rightarrow x=\frac{52}{4} \Rightarrow x=13$$
 
Solving……
Multiply second equation with 2 then
-4x + 6y =2………………….(2)
Now add (1) ,(2)
U will get y value and then substitute y value in (1) or (2)
U will get x value
This is the method for solve any 2 equations…………..keep practcing
 
john123 said:
U will get y value and then substitute y value in (1) or (2)
U will get x value
Just a comment. As "U" has a specific meaning to it ("U" is defined to be the "union" operator) I recommend that you please type out the whole word "you."

-Dan
 
Thanks for your suggestion.I will rectify my mistake.
 

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