Question

Solve the given question in a detail manner:
Write equations for the following statement:
\[2\] subtract from \[y\] is \[8\].

Answer 1

Hint: Define what a linear equation is then write the given statement in the form of mathematical expression. Solve the linear equation to find the unknown variable by bringing the constants to one side and the variables to another side.

Complete step-by-step solution:
Linear equations are in the form \[{a_1}{x_1} + {a_2}{x_2} + {a_3}{x_3} + ... + {a_n}{x_n} + b = 0\], where \[{x_1},{x_2},{x_3}...,{x_n}\] are the variables and the \[{a_1},{a_2},{a_3}...,{a_n}\] are the coefficient of the variables. The coefficient of the variables might be real numbers mostly. The co-efficient is also considered as the parameter of the equations. To obtain a linear equation, we equate the equation to zero. It is a linear polynomial over a field from which the coefficients are taken.
The solution is found by solving the constant terms.
We are given \[2\] subtract from \[y\] is \[8\].
That implies \[2\] is subtracted from \[y\] which is equated to \[8\]
\[ \Rightarrow y - 2 = 8\]
The constants are taken to the left-hand side.
\[ \Rightarrow y = 8 + 2\]
Adding the left-hand side terms, we get;
\[ \Rightarrow y = 10\]
Therefore, \[y = 10\]

Equation for the given statements is y-2=8 and the simplified equation will be y=10.

Note: The equation is a linear equation which is expressed in the form of one variable as \[ax + b = 0\] where \[a\] and \[b\] are two integers which are coordinates of the variable. This equation is a one-degree variable which is why we can perform linear algebraic operations. Mostly the term linear equation is referring implicitly to the case of one variable only. There can only be a single, unique solution for a linear equation. There can be infinitely many solutions for the linear equation for the two variable equations.