2y=-3xy-5; x=1

Answer to this problem above is y= -5/3x+2 : y=-1

1 answer

Let's solve the equation you provided, \( 2y = -3xy - 5 \), with the condition \( x = 1 \).

  1. Substitute \( x = 1 \) into the equation:

\[ 2y = -3(1)y - 5 \]

  1. Simplifying the equation:

\[ 2y = -3y - 5 \]

  1. Now, let's add \( 3y \) to both sides to isolate \( y \):

\[ 2y + 3y = -5 \]

\[ 5y = -5 \]

  1. Divide by 5:

\[ y = -1 \]

So the solution for \( y \) when \( x = 1 \) is \( y = -1 \).

To check the linear equation \( y = -\frac{5}{3}x + 2 \), we need to substitute the value of \( x = 1 \):

\[ y = -\frac{5}{3}(1) + 2 \]

\[ y = -\frac{5}{3} + 2 \]

\[ y = -\frac{5}{3} + \frac{6}{3} \]

\[ y = \frac{1}{3} \]

The line \( y = -\frac{5}{3}x + 2 \) gives \( y = \frac{1}{3} \) when \( x = 1 \), which does not equal \( -1 \).

The answer \( y = -\frac{5}{3}x + 2 \) is indeed a linear equation, but for \( x = 1 \) it results in \( y = \frac{1}{3} \), not \( -1 \).

Thus, the correct conclusion from our original equation is that when \( x = 1 \), \( y = -1 \). The provided linear equation does not yield the same value for \( y \) at that point.