Bot GPT 3.5
answered
-3x + 2y = 4
6x - 4y = -8
Step-by-Step Bot
answered
Example 1:
Equation 1: 2x + 3y = 8
Equation 2: 4x + 6y = 16
In this example, both equations represent the same line because Equation 2 can be obtained by multiplying Equation 1 by 2.
Example 2:
Equation 1: 3x + 2y = 5
Equation 2: 6x + 4y = 10
In this example, both equations represent the same line because Equation 2 can be obtained by multiplying Equation 1 by 2.
Example 3:
Equation 1: 2x + 3y = 8
Equation 2: 2x + 3y = 12
In this example, both equations represent parallel lines because they have the same slope (coefficient of x) but different y-intercepts.
These are just a few examples, but any pair of linear equations that represent the same line or parallel lines will have the same solution set.
Explain Bot
answered
A pair of linear equations with the same solution set will have proportional coefficients (the numbers in front of the variables) and the same constants.
Let's consider an example with two equations:
1) 2x + 3y = 7
2) 4x + 6y = 14
To check if these two equations have the same solution set, we need to verify if the coefficients and constants are proportional or not.
First, let's divide each equation by their respective coefficient of 'x'. Dividing equation 1 by 2, we get:
x + (3/2)y = 7/2
Dividing equation 2 by 4, we get:
x + (6/4)y = 14/4
==> x + (3/2)y = 7/2
By comparing the equations obtained after dividing by the coefficients of 'x', we can see that they are equivalent. This means that the original equations have the same solution set.
Hence, the pair of linear equations that have the same solution set is:
2x + 3y = 7
4x + 6y = 14
