Question

$3x-1=y$, $4x-1=y$
Consider the system of equations above. Which of following statement about this system is true?

• A. There is only one $(x,y)$ solution & $y$ is positive.
• B. There is only one $(x,y)$ solution & $y$ is negative
• C. There are infinitely many $(x,y)$ solutions
• D. There are no $(x,y)$ solutions

Answer 1

The correct option is B There is only one $(x,y)$ solution & $y$ is negative

As we can see both the equations are given in terms of $y$. So let's equate them
$3x-1=4x-1$
$3x=4x$
$x=0$
Now that we know $x$, we can substitute this value into the first equation to find $y$
$2\left(0\right)-1=y$
$-1=y$
Therefore $y$ is negative
This is only one $(x,y)$ solution and $y$ is negative.