Question

How do you write $ y+1=x+2$ in standard form?

Answer 1

Hint: To write a linear equation with two variables in standard form, we need to equate the variable terms to the constant terms. The expression in standard form for a linear equation with variables x and y and integers a, b, and c is given as $ ax+by=c$.To solve this problem, we will have to write $ y+1=x+2$ in the form $ ax+by=c$. To do this, we can simply subtract 1 from both sides and then subtract x from both sides.

Complete step by step answer:
From the problem, we are asked to write $ y+1=x+2$ in standard form
Let us consider $ y+1=x+2\,\cdots \cdots \cdots \cdots (1)$
To express $ y+1=x+2$ in standard form, we need to write it in the form $ ax+by=c$. To do this, we will have to make sure that all the variable terms are on one side of the equation and all the constant terms are on the other side of the equation.
Let us subtract 1 from both sides of equation (1), so we get
$ \Rightarrow y=x+1\,\cdots \cdots \cdots \cdots (2)$
Now, let’s subtract x from both sides of equation (2), so we get
 $ \Rightarrow y-x=1\,\cdots \cdots \cdots \cdots (3)$
Now, we can see that equation (3) is expressed in the form $ ax+by=c$. Hence, we get $ y+1=x+2$ in standard form as $ y-x=1\,$
$ \therefore y+1=x+2$ is written as $ y-x=1\,$ in standard form.

Note:
It is important to note that when solving problems like this care should be taken when arranging the variable terms and the constant terms as signs change when either of the terms crosses over the equality sign. We might end up getting our answers like $ x-y=-1\,$ which is also correct and standard form. It is also very important to note that polynomials of higher degrees can also be expressed in standard form and this is done by simply rearranging the polynomial in decreasing order of the degrees.