An equation is a mathematical statement that may (or may not) be true, defined for some variables. Solving an equation is finding those values of the variables for which the equation or statement is true.
The result of solving an equation is called the solution. It is the value or set of values that satisfy the equation, making both sides equal when substituted into it. In the context of algebra, solutions can be numbers, variables, or expressions that fulfill the given mathematical condition.
The variables of this equation are your letters: a, b, and c. Variables merely stand in an equation to represent values that we don't know. "Solving" an equation is the process by which we uncover those values. In this particular case, since there are three variables, we cannot discover their values unless we have two other equivalent equations (a system of equations).
If we are talking about the algebraic expressions, then an expression can be simplified or be evaluated for specific values of its variables, while an equation need to be solved, in other words to find the values of the variables that make the equation a true statement. If we are solving an equation, then we can work in the same way that we can simplify an expression (since an equation is a statement that states that two expressions are equal), or factoring an expression.
A solution to an equation is a set of values for the variables in the equation which make it true.
An equation is a mathematical statement that may (or may not) be true, defined for some variables. Solving an equation is finding those values of the variables for which the equation or statement is true.
The result of solving an equation is called the solution. It is the value or set of values that satisfy the equation, making both sides equal when substituted into it. In the context of algebra, solutions can be numbers, variables, or expressions that fulfill the given mathematical condition.
The variables of this equation are your letters: a, b, and c. Variables merely stand in an equation to represent values that we don't know. "Solving" an equation is the process by which we uncover those values. In this particular case, since there are three variables, we cannot discover their values unless we have two other equivalent equations (a system of equations).
You are trying to find a set of values such that, if those values are substituted for the variables, every equation in the system is true.
If an equation has two variables, we'll call them (x,y), the variables can be any value as long as both sides of the equation have the same result. If the equation was x = y, then the variables could be (1,1), (2,2), (3,3),etc...
the relationship between variables and/or variables and values
If we are talking about the algebraic expressions, then an expression can be simplified or be evaluated for specific values of its variables, while an equation need to be solved, in other words to find the values of the variables that make the equation a true statement. If we are solving an equation, then we can work in the same way that we can simplify an expression (since an equation is a statement that states that two expressions are equal), or factoring an expression.
It is the set of values for all the variables in the equation which make the equation true.
A solution to an equation is a set of values for the variables in the equation which make it true.
An equation that is always true is an identity.
The solution to an equation consists of the value (or values) of all the variables such that the equation is true when the variable(s) take those values.
A linear system is a set of equations where each equation is linear, meaning it involves variables raised to the power of 1. Solving a linear system involves finding values for the variables that satisfy all the equations simultaneously. This process is used to find solutions to equations with multiple variables by determining where the equations intersect or overlap.