The lines $y=5x+3$, $y=-2x-25$ and $y=3x+k$ intersect at the same point. What is the value of $k$?
I want to find the value of $k$ that makes the line $y=3x+k$ pass through the point of intersection of the other two lines. To do that, I need to find the coordinates of the point of intersection of the lines $y=5x+3$ and $y=-2x-25$. I can use the substitution method to solve for $x$ and $y$. I can substitute $y=5x+3$ into the equation $y=-2x-25$ and get $5x+3=-2x-25$. Simplifying, I get $7x=-28$, so $x=-4$. Then, I can plug in $x=-4$ into either equation to get $y$. I'll use $y=5x+3$ and get $y=5(-4)+3=-17$. So the point of intersection of the first two lines is $(-4,-17)$. Now, I need to find the value of $k$ that makes the line $y=3x+k$ pass through this point. I can substitute $x=-4$ and $y=-17$ into the equation $y=3x+k$ and get $-17=3(-4)+k$. Simplifying, I get $k=-5$. 