What is the value of x+y-2z?

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).

Citations

  1. 1. Khan Academy – Algebra
  2. 2. Purplemath – Solving Equations
  3. 3. Math is Fun – Order of Operations