Find the value of \( y \) that makes each equation true for all values of \( x \) 13. \( 3 x+6 x=y x \) 14. \( x+5+11 x= \)

Let's solve each equation to find the value of \( y \) that makes the equation true for all values of \( x \). ### Problem 13 **Equation:** \[ 3x + 6x = yx \] **Solution:** Combine like terms on the left side: \[ (3 + 6)x = yx \] \[ 9x = yx \] For this equation to be true for all values of \( x \), the coefficients of \( x \) on both sides must be equal: \[ y = 9 \] **Answer:** \( y = 9 \) --- ### Problem 14 **Equation:** \[ x + 5 + 11x = \text{(missing right-hand side)} \] It seems there might be a part of the equation missing on the right-hand side. However, if we interpret the equation as needing to be equal to \( yx \), the equation would look like: \[ x + 5 + 11x = yx \] \[ 12x + 5 = yx \] **Solution:** For the equation \( 12x + 5 = yx \) to hold true for all values of \( x \), the coefficients of \( x \) must be equal, and the constant terms must also be equal: \[ 12 = y \quad \text{and} \quad 5 = 0 \] The second condition \( 5 = 0 \) is impossible, which means there is **no value of \( y \)** that satisfies this equation for all \( x \). **Answer:** - **Problem 13 Answer:** \( y = 9 \) - **Problem 14 Answer:** No such value of \( y \) exists.