Question

How do you evaluate $xy - z$ , when $x = - 2$ , $y = 3$ and $z = 1$ ?

Answer 1

Hint: To solve the algebraic expression for the given values, substitute the values of variables in the expression and then simplify the expression using the BODMAS rule, that is in the given expression first perform multiplication and then subtraction.

Complete step-by-step solution:
The given expression is $xy - z$ and given values are $x = - 2$ , $y = 3$ and $z = 1$ .
We know $xy = x \times y$ , so we can write the expression as:
$ \Rightarrow x \times y - z$
Now, substitute the value of $x$ , $y$ , $z$ in the expression one by one:
$ \Rightarrow x \times y - z$
Substitute $x = - 2$ :
$ \Rightarrow - 2 \times y - z$
Substitute $y = 3$ :
$ \Rightarrow - 2 \times 3 - z$
Substitute $z = 1$ :
$ \Rightarrow - 2 \times 3 - 1$
First, simplify the product:
$ \Rightarrow - 6 - 1$
Subtract the numbers:
$ \Rightarrow - 7$

Therefore, the solution of the given expression $xy - z$ when $x = - 2$ , $y = 3$ and $z = 1$ is $ - 7$.

Additional Information: Algebraic expression is an expression that is made up of constants and variables along with algebraic operations like addition, subtraction, multiplication, or division that is an expression is a combination of numbers, variables, and operations.

Note: Alternate method to solve the expression by assigning the terms in expression another variable and then combine all these variables. In the given expression $xy - z$ , we may consider:
$a = xy - z$
Again in the expression $a = xy - z$ , we may consider $b = xy$ , so that expression will become:
$ \Rightarrow a = b - z$
Again in the expression $ \Rightarrow a = b - z$ , we may consider $c = z$ , so that final expression will become:
$ \Rightarrow a = b - c$
Now consider $b = xy$:
Substitute $x = - 2$ and $y = 3$ in the expression:
$b = - 2 \times 3$
$ \Rightarrow b = - 6$
Substitute the value of the variable $b$ into the expression $a = b - c$:
$ \Rightarrow a = - 6 - c$
Now, calculate the value of the variable $c$ and substitute in the above expression.
We have $c = z$ :
Substitute $z = 1$:
$\therefore c = 1$
Substitute the value of the variable $c$ into the expression $a = - 6 - c$:
$ \Rightarrow a = - 6 - 1$
By simplifying the right side of the equation, we get:
$a = - 7$
But $a$ is nothing but given expression itself, that is $a = xy - z$ , which shows that the value of the given expression $xy - z$ is $ - 7$ . i.e.
The solution of the given expression $xy - z$ when $x = - 2$ , $y = 3$ and $z = 1$ is $ - 7$.