To determine the value of the expression $x + y – 2z$, we need to know the values of $x$, $y$, and $z$. Without specific values or additional context, we can’t calculate an exact numerical answer. However, let’s explore how we can approach solving such an expression in different scenarios.
Scenario 1: Given Values
If we have specific values for $x$, $y$, and $z$, we can simply substitute them into the expression and perform the arithmetic operations.
Example
Suppose $x = 3$, $y = 5$, and $z = 2$
Substitute these values into the expression:
$x + y – 2z = 3 + 5 – 2(2)$
First, multiply $2$ by $2$:
$3 + 5 – 4$
Then, add $3$ and $5$:
$8 – 4$
Finally, subtract $4$ from $8$:
$4$
So, the value of $x + y – 2z$ is $4$ when $x = 3$, $y = 5$, and $z = 2$
Scenario 2: Solving Equations
Sometimes, we might be given equations that relate $x$, $y$, and $z$. In such cases, we can solve these equations to find the values of $x$, $y$, and $z$, and then substitute them into the expression.
Example
Suppose we have the following system of equations:
$x + y = 10$
$x – z = 3$
$2y + z = 12$
We can solve these equations step by step.
First, solve the first equation for $y$:
$y = 10 – x$
Next, substitute $y = 10 – x$ into the third equation:
$2(10 – x) + z = 12$
Simplify and solve for $z$:
$20 – 2x + z = 12$
$z = 12 – 20 + 2x$
$z = 2x – 8$
Now, substitute $z = 2x – 8$ into the second equation:
$x – (2x – 8) = 3$
Simplify and solve for $x$:
$x – 2x + 8 = 3$
$-x + 8 = 3$
$-x = 3 – 8$
$-x = -5$
$x = 5$
Now, substitute $x = 5$ back into the first and third equations to find $y$ and $z$:
$y = 10 – 5 = 5$
$z = 2(5) – 8 = 10 – 8 = 2$
So, $x = 5$, $y = 5$, and $z = 2$. Substitute these values into the expression $x + y – 2z$:
$5 + 5 – 2(2) = 5 + 5 – 4 = 10 – 4 = 6$
Thus, the value of $x + y – 2z$ is $6$ when $x = 5$, $y = 5$, and $z = 2$
Conclusion
The value of the expression $x + y – 2z$ depends on the values of $x$, $y$, and $z$. By substituting known values or solving related equations, we can determine the specific value of the expression in different scenarios. Always remember to follow the order of operations: parentheses, exponents, multiplication and division (from left to right), and addition and subtraction (from left to right).