Question

How do you simplify \[3a + 4b - 2a - b\] ?

Answer 1

Hint: To simplify the given expression, we know that the algebraic expression should be any one of the forms such as addition, subtraction, multiplication and division. The given equation is a linear equation as there is a constant variable involved and to solve this equation, combine all the like terms and then simplify the terms.

Complete step-by-step solution:
Let us write the given equation:
\[\Rightarrow 3a + 4b - 2a - b\]
As the equation consists of like terms, so combine all the like terms as:
\[\Rightarrow 3a + 4b - 2a - b\]
\[ \Rightarrow \] \[1a + 4b - b\]
Now multiplying 1 we get
\[\Rightarrow a + 4b - b\]
As the obtained equation consists of like terms, so combine all the like terms and simplify:
\[\Rightarrow a + 4b - b\]
Therefore, after simplifying we get
\[\Rightarrow a + 3b\]

Therefore the simplified equation is a + 3b.

Additional information:
Equations that have more than one unknown can have an infinite number of solutions, finding the values of letters within two or more equations are called simultaneous equations because the equations are solved at the same time.

Solving simultaneous equations by Substitution: The substitution method is the algebraic method to solve simultaneous linear equations. As the word says, in this method, the value of one variable from one equation is substituted in the other equation. In this way, a pair of the linear equations gets transformed into one linear equation with only one variable, which can then easily be solved.

Note: The key point to solve this type of equation is to combine all the like terms and evaluate for the variable asked. As we know that Simultaneous equations are two equations, each with the same two unknowns and are simultaneous because they are solved together and there are three methods to solve the system of linear equations in two variables are: Substitution method, Elimination method and cross-multiplication method.