Question

If 2x + y = 9 and y - z = 4 then 2x + z = ?

• A. 5
• B. 13
• C. Cannot be determined
• D. 29
• E. 21

Hint:

When you are asked to find the value of an expression (like 2x + z) rather than the individual variables, look for a way to combine the given equations directly to form that expression. This is often faster than solving for each variable separately.

Answer 1

The Correct Option is A

Step 1: Understanding the Concept:
We are given a system of two linear equations with three variables. We need to find the value of a specific expression involving two of these variables. This can often be done by manipulating and combining the given equations to eliminate the third variable.
Step 2: Key Formula or Approach:
We can use the substitution or elimination method. The goal is to eliminate the variable \(y\), which appears in both equations, to find a relationship between \(x\) and \(z\).
Equation 1: \(2x + y = 9\)
Equation 2: \(y - z = 4\)
Step 3: Detailed Explanation:
Method 1: Substitution
From Equation 1, isolate y: \[ y = 9 - 2x \] Substitute this expression for y into Equation 2: \[ (9 - 2x) - z = 4 \] Now, we want to find the value of \(2x + z\). Let's rearrange the equation: \[ 9 - 4 = 2x + z \] \[ 5 = 2x + z \] Method 2: Elimination
Rearrange Equation 2 to align the variables: \[ y = 4 + z \] Now we have: \[ 2x + y = 9 \] \[ y = 4 + z \] Rewrite Equation 2 as \(-y + z = -4\). Let's rewrite Equation 1 as \(y = 9 - 2x\). Set the two expressions for y equal to each other: \[ 9 - 2x = 4 + z \] Rearrange to find \(2x + z\): \[ 9 - 4 = 2x + z \] \[ 5 = 2x + z \] Step 4: Final Answer:
The value of \(2x + z\) is 5.