State whether the lines are parallel, perpendicular, or neither. Show your work.x–5y=103 and –2x=–206–10y
i got neither is that right
divide 2nd by -2 ... x = 103 + 5y
subtract 5y ... x - 5y = 103
they are the same line
The Answer is Coinciding
To determine if two lines are parallel, perpendicular, or neither, we need to examine their slopes.
The given equations are:
1) x - 5y = 103
2) -2x - 10y = -206
First, let's rewrite both equations in slope-intercept form (y = mx + b), where "m" represents the slope:
1) x - 5y = 103
-5y = -x + 103
y = (1/5)x - 103/5
2) -2x - 10y = -206
-10y = 2x - 206
y = -(1/5)x + 103/5
By examining the coefficients of "x" in both equations, we can determine that their slopes are 1/5 and -1/5, respectively.
Since the slopes of the two lines are negative reciprocals of each other (1/5 and -1/5), the lines are perpendicular to each other.
Therefore, your answer of "neither" is incorrect. The correct answer is that the lines are perpendicular.