Question

If 7x-5y=2 and 3x+y=4, then x=?

• A. 3
• B. -3
• C. 1
• D. 2

Answer 1

The Correct Option is C

To solve the problem, we need to find the value of \( x \) given the system of linear equations:

\[ 7x - 5y = 2 \] \[ 3x + y = 4 \] Step 1: Solve for \( y \) in terms of \( x \) from the second equation. From the second equation: \[ 3x + y = 4 \] Subtract \( 3x \) from both sides: \[ y = 4 - 3x \] Step 2: Substitute \( y = 4 - 3x \) into the first equation. The first equation is: \[ 7x - 5y = 2 \] Substitute \( y = 4 - 3x \): \[ 7x - 5(4 - 3x) = 2 \] Step 3: Simplify the equation. Distribute the \(-5\): \[ 7x - 20 + 15x = 2 \] Combine like terms: \[ 22x - 20 = 2 \] Step 4: Solve for \( x \). Add 20 to both sides: \[ 22x = 22 \] Divide by 22: \[ x = 1 \] Step 5: Verify the solution. Substitute \( x = 1 \) back into the expression for \( y \): \[ y = 4 - 3x = 4 - 3(1) = 4 - 3 = 1 \] Now check both equations: 1. For \( 7x - 5y = 2 \): \[ 7(1) - 5(1) = 7 - 5 = 2 \] (True) 2. For \( 3x + y = 4 \): \[ 3(1) + 1 = 3 + 1 = 4 \] (True) Both equations are satisfied, so the solution is correct.

Final Answer: \[ {1} \]