<h3>Linear Equations</h3>
Linear equations are used to relate equations that have constant slopes and rates of change
A linear equation is represented as:
Where:
- m represents the slope
- b represents the y-intercept
<h3>Parallel lines</h3>
When two lines are parallel, then both lines will have the same slope
<h3>Perpendicular lines</h3>
When two lines are perpendicular, then the slopes of both lines will be opposite reciprocal
<h3>Same lines</h3>
Same lines will have the same slope and the same intercepts
Using the above highlights, we can now determine the relationship between the given system of linear equations
<h3>
1. Equations y=-x+2 and 2y = 6x +8
</h3>
We have:
and
Divide through by 2
The above means that, the system of equations are neither parallel nor perpendicular.
Also, both lines are not the same line, but they are intersecting lines and only one solution exists between the system
<h3>
2. Equations y =7-3x and y = 7+3x
</h3>
We have:
and
The above means that, the system of equations are neither parallel nor perpendicular.
Also, both lines are not the same line, but they are intersecting lines and only one solution exists between the system
<h3>
3. Equations y = 3x - 2 and y = 3x + 6
</h3>
We have:
and
The above means that, the system of equations are parallel; this is so because they have the same slope of 3
Also, both lines are not the same line, and they do not intersect;
So, no solution exists between the system
<h3>
4. Equations y = (x + 2) - 4 and y = 4x - 5</h3>
We have:
and
Open bracket
So, we have:
and
The above means that, the system of equations are neither parallel nor perpendicular.
Also, both lines are not the same line, but they are intersecting lines and only one solution exists between the system
<h3>
4. Equations 8x + y = 3 and 3x = 12</h3>
We have:
and
Make y the subject, and solve for x
So, we have:
and
The above means that, the system of equations are neither parallel nor perpendicular.
Also, both lines are not the same line, but they are intersecting lines and only one solution exists between the system
Read more about linear equations at:
brainly.com/question/14323743