Question

If \( 3y + x > 2 \) and \( x + 2y \leq 3 \), what can be said about the value of \( y \)?

• A. \( y = -1 \)
• B. \( y > -1 \)
• C. \( y < -1 \)
• D. \( y = 1 \)
• E.

Hint:

When solving inequalities, always substitute expressions from one inequality into the other to simplify and solve.

Answer 1

The Correct Option is B

Starting with the second inequality \( x + 2y \leq 3 \), we solve for \( x \): \[ x \leq 3 - 2y \] Step 1: Substitute this expression for \( x \) into the first inequality: \[ 3y + (3 - 2y)>2 \] Step 2: Simplifying the inequality: \[ 3y + 3 - 2y>2 \] \[ y + 3>2 \] Step 3: Solving for \( y \): \[ y>-1 \] Thus, the solution is \( y>-1 \).