Question:
If \( 3x + 2y = 6 \) and \( 2x - y = 4 \), what is \( x + y \)?
If \( 3x + 2y = 6 \) and \( 2x - y = 4 \), what is \( x + y \)?
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When solving a system of linear equations, you can use substitution or elimination to solve for the variables.
Updated On: Oct 6, 2025
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The Correct Option is B
Solution and Explanation
We are given the system of equations:
\[
3x + 2y = 6
\cdots (1) \] and \[ 2x - y = 4
\cdots (2). \] Step 1: Solve equation (2) for \( y \): \[ 2x - y = 4
\Rightarrow
y = 2x - 4. \] Step 2: Substitute \( y = 2x - 4 \) into equation (1): \[ 3x + 2(2x - 4) = 6. \] Simplify: \[ 3x + 4x - 8 = 6
\Rightarrow
7x - 8 = 6. \] Step 3: Solve for \( x \): \[ 7x = 14
\Rightarrow
x = 2. \] Step 4: Substitute \( x = 2 \) into \( y = 2x - 4 \) to find \( y \): \[ y = 2(2) - 4 = 4 - 4 = 0. \] Step 5: Now, find \( x + y \): \[ x + y = 2 + 0 = 2. \] Thus, the value of \( x + y \) is \( 1 \).
\cdots (1) \] and \[ 2x - y = 4
\cdots (2). \] Step 1: Solve equation (2) for \( y \): \[ 2x - y = 4
\Rightarrow
y = 2x - 4. \] Step 2: Substitute \( y = 2x - 4 \) into equation (1): \[ 3x + 2(2x - 4) = 6. \] Simplify: \[ 3x + 4x - 8 = 6
\Rightarrow
7x - 8 = 6. \] Step 3: Solve for \( x \): \[ 7x = 14
\Rightarrow
x = 2. \] Step 4: Substitute \( x = 2 \) into \( y = 2x - 4 \) to find \( y \): \[ y = 2(2) - 4 = 4 - 4 = 0. \] Step 5: Now, find \( x + y \): \[ x + y = 2 + 0 = 2. \] Thus, the value of \( x + y \) is \( 1 \).
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