Question

Line

Answer 1

Linear Equations

Linear equations are used to relate equations that have constant slopes and rates of change

A linear equation is represented as:

$y = mx + b$

Where:

• m represents the slope
• b represents the y-intercept

Parallel lines

When two lines are parallel, then both lines will have the same slope

Perpendicular lines

When two lines are perpendicular, then the slopes of both lines will be opposite reciprocal

Same lines

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

1. Equations y=-x+2   and 2y = 6x +8

We have:

$y = -x +2$

and

$2y = 6x +8$

Divide through by 2

$y = 3x +4$

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

2. Equations y =7-3x   and y = 7+3x

We have:

$y = 7-3x$

and

$y = 7 + 3x$

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

3. Equations y = 3x - 2   and y = 3x + 6

We have:

$y = 3x - 2$

and

$y = 3x + 6$

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

4. Equations y = (x + 2) - 4   and y = 4x - 5

We have:

$y=(x + 2) - 4$

and

$y = 4x - 5$

Open bracket

$y =x + 2 - 4$

$y =x - 2$

So, we have:

$y =x - 2$ and $y = 4x - 5$

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

4. Equations 8x + y = 3   and 3x = 12

We have:

$8x + y = 3$

and

$3x = 12$

Make y the subject, and solve for x

$8x + y = 3$

$y = -8x + 3$

$3x = 12$

$x=4$

So, we have:

$y = -8x + 3$ and $x=4$

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:

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