Question

Evaluate the following expression \[\dfrac{y}{{z - x}} + 3\;\;\;{\text{when}}\;x = 3,y = 4\;{\text{and}}\;z = 5\].

Answer 1

Hint: The given expression is an expression with more than one variable. For solving equations with more than one variable we need at least two equations. Here simple substitution of the given values in the given expression can be used for the process of evaluation.So we just need to substitute or plug in the given values and thus evaluate the given expression.

Complete step by step solution:
Given, \[\dfrac{y}{{z - x}} + 3........................\left( i \right)\]
We need to evaluate (i) at \[x = 3,y = 4\;{\text{and}}\;z = 5\]. Now we know that for solving equations with more than one variable we need at least two equations. But here the values of each variable have been given such that we just need to simply substitute or just plug in the values of $x,y,z$ in the given expression.

Now let’s substitute \[x = 3,y = 4\;{\text{and}}\;z = 5\]in the expression (i).
Such that we can write:
\[\dfrac{y}{{z - x}} + 3 = \dfrac{4}{{5 - 3}} + 3........................\left( {ii} \right)\]
Now on just simplifying the equation (ii) we can get the final answer, such that:
\[\dfrac{y}{{z - x}} + 3 = \dfrac{4}{{5 - 3}} + 3 \\
\Rightarrow\dfrac{y}{{z - x}} + 3 = \dfrac{4}{2} + 3 \\
\Rightarrow\dfrac{y}{{z - x}} + 3 = 2 + 3 \\
\therefore\dfrac{y}{{z - x}} + 3= 5......................\left( {iii} \right) \\ \]
Therefore on evaluating \[\dfrac{y}{{z - x}} + 3\;\;\;{\text{when}}\;x = 3,y = 4\;{\text{and}}\;z = 5\] we get the final answer as $5$.

Additional Information:
If we are given a pair of linear equations it is solved either by graphical or algebraic method. The algebraic method is of three types:
1. Substitution Method
2. Elimination Method
3. Cross Multiplication Method
Depending on the type of question we have to choose the method and thus solve the given question.

Note: Similar questions of these types have to be solved as shown above. Here there are three variables and also the values of those three variables are given such that the only work we have to do is simple substitution of the values. While in the case of solving a pair of linear equations we need to express the two linear equations in two different variables and then proceed.