Standard form of Linear Equations in Two Variables


 
 
Concept Explanation
 

Standard form of Linear Equations in Two Variables

The Standard Form for a linear equation in two variables, x and y, is usually given as :  ax + by = c,  where a, b and c are real numbers, and a and b are not both zero.

If we have a linear equation in slope-intercept form,  y = m x + b

For example, 3x + 2y = 8 is a linear equation in two variables.

Illustration: Convert y=frac{8}{3}x+5  in standard form :

Solution :  The given equation,y=frac{8}{3}x+5 ,  

  • Place all the variables on one side : y-frac{8}{3}x=5
  • To simplify the terms, divide each term by 3:
  • ytimes 3-frac{8}{3}xtimes 3=5times 3

    We get , 3y - 8x = 15,

    So as we know,   ax + by = c is the standard form, the final answer is -8x + 3y = 15

    Sample Questions
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    Question : 1

    What is the standard form of the linear equation 3x-y+1-2x=0?

    Right Option : C
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    Question : 2

    Which of the following is the standard form of linear equation  in two variables ?

         

                      

    Right Option : D
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    Question : 3

    Write each of the following equations in the form  ax+by+c=0  and indicate the values of a,b and c in : large 7x-5=2y

    Right Option : B
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