Is the following pair of lines paralle or perpendicular? Prove the answer.

2y-x=2
y+2x=4

I think that the lines are perpendicular but do not know how to work the problem.
x=6/5 y=8/5 Can some one show me how to work this equation?

x=6/5 y=8/5 are the coordinates of the intersection point, but that does not tell you if the lines are perpendular or not.

The slope of the first line is 1/2.
The slope of the second line is -2.

Because the product of the slopes is -1, they are perpendicular.

To determine whether the given pair of lines is parallel or perpendicular, we need to examine the slope of each line. If the slopes are equal, the lines are parallel. If the slopes are negative reciprocals of each other, the lines are perpendicular.

To find the slope of a line in standard form (Ax + By = C), we can rewrite the equation in slope-intercept form (y = mx + b), where m is the slope.

Let's start by rewriting the given pair of lines in slope-intercept form:

1) 2y - x = 2
Rearranging the equation, we get: 2y = x + 2
Dividing by 2, we have: y = (1/2)x + 1

2) y + 2x = 4
Rearranging the equation, we get: y = -2x + 4

Now that we have both equations in slope-intercept form, we can determine their slopes.

The slope of the first line (equation 1) is (1/2), and the slope of the second line (equation 2) is -2.

To prove if they are parallel or perpendicular, we need to check if these slopes are equal or negative reciprocals of each other.

Since the slopes (1/2) and -2 are neither equal nor negative reciprocals, we can conclude that the given pair of lines is neither parallel nor perpendicular.

Now, to find the solution to the system of equations, we can solve them simultaneously. We have:

1) y = (1/2)x + 1
2) y = -2x + 4

To solve, we can set the right sides of both equations equal to each other:

(1/2)x + 1 = -2x + 4

To isolate the x-term, we can subtract (1/2)x and 1 from both sides:

(1/2)x + 1 - (1/2)x - 1 = -2x + 4 - (1/2)x - 1
Simplifying, we get:

0 = -2.5x + 3

Now, we can isolate the x-term by subtracting 3 from both sides:

-3 = -2.5x

Finally, we can solve for x by dividing both sides by -2.5:

x = -3 / -2.5
x = 6/5

To find the corresponding value of y, we can substitute the value of x back into one of the original equations. Let's use equation 1:

2y - x = 2

Substituting x = 6/5, we have:

2y - 6/5 = 2

To isolate y, we can add 6/5 to both sides:

2y = 2 + 6/5

Simplifying, we get:

2y = 10/5 + 6/5
2y = 16/5

Finally, dividing both sides by 2, we find:

y = 16/10
y = 8/5

Therefore, the solution to the given pair of equations is x = 6/5 and y = 8/5.