In a pig race, your pig has a head start of 3 feet and is running at a rate of 2 feet per second. Your friend’s pig also runs at a rate of 2 feet per second. A system of linear equations that represents this situation is $y=2x+3$ and $y=2x$ . Does your friend’s pig catch up to your pig?

Question

In a pig race, your pig has a head start of 3 feet and is running at a rate of 2 feet per second. Your friend’s pig also runs at a rate of 2 feet per second. A system of linear equations that represents this situation is $y=2x+3$ and $y=2x$ . Does your friend’s pig catch up to your pig?

Answer 1

To determine if your friend's pig catches up to your pig, we need to find the point of intersection of the two linear equations. In other words, we need to find the values of x and y where both equations are true.

Substitute the second equation $y=2x$ into the first equation $y=2x+3$:

$2x = 2x + 3$

Subtracting $2x$ from both sides gives us:

$0 = 3$

This is a contradiction, so the two equations do not intersect at any point. This means that your pig, with a head start of 3 feet, will always remain 3 feet ahead of your friend's pig, as both pigs run at the same rate of 2 feet per second. Therefore, your friend's pig will not catch up to your pig.