Question

Identify any two equations that form a system with one solution (different slopes) ? [ Hint: Make sure all equations are in Y=mx + b format first. ] *

Answer 1

To create a system of equations with one solution, we need to ensure that the two lines represented by the equations intersect at a single point. This is true when the lines have different slopes. Here are two equations in the form \( y = mx + b \):

1. \( y = 2x + 3 \) (slope \( m = 2 \))
2. \( y = -1x + 1 \) (slope \( m = -1 \))

These equations have different slopes (\( 2 \) and \( -1 \)), which means they will intersect at one point, creating a system with one solution.