Question

How do you write 4y-5x=3(4x-2y+1) in standard form?

Answer 1

Hint: In this type of question, we will first expand the terms in the parenthesis on the right side of the equation by multiplying each term within the parenthesis by the term outside the parenthesis. As we know that every linear equation is of the form Ax+By=C. Therefore, we will make the equation in the form of Ax+By=C. After that, we will get the solution in the standard form.

Complete step by step answer:
Let us solve the question.
Let us expand the terms in the parenthesis which is given on the right side of the equation
4y-5x=3(4x-2y+1)
Now, we will multiply each of the terms within the parenthesis by the term outside the parenthesis.
4y-5x=3(4x)-3(2y)+3(1)
\[\Rightarrow \]4y-5x=12x-6y+3
We know that the standard form of a linear equation is: Ax+By=C
Where, if at all possible A,B, and C are integers, and A is non-negative, and A,B, and C have no common factors other than 1.
To convert to the Standard Form of a linear equation we need to first subtract 12x and add 6y to each side of the equation to get the x and y terms on the left side of the equation while keeping the equation balanced:
\[-12x+6y+4y-5x=-12x+6y+12x-6y+3\]
\[\Rightarrow -12x-5y+6y+4y=-12x+12x+6y-6y+3\]
\[\Rightarrow (-12-5)x+(6+4)y=0-0+3\]
\[\Rightarrow -17x+10y=3\]
Now, we will multiply each side of the equation by -1 to make the coefficient of the x as a positive integer according to the standard form of a linear equation.
\[-1(-17x+10y)=-1(3)\]
\[\Rightarrow 17x-10y=-3\]

Note:
 Students can make silly mistakes here. There can be multiplying mistakes to be made by students. Be careful of the signs while solving the problems. For example, in this equation \[-1(-17x+10y)=-1(3)\], at the time of multiplying, someone can make mistake here. So, one should be aware of that.