Solve for y and determine if the lines are parallel, perpendicular or neither?

Question

{6x=5y+1
{-12x+10y=1


Would I Multiply 6x by 12 and vice versa with -12x by 6x?Distribute and then solve?

Answer 1

"Solve for y," means "put in slope-intercept form." (i.e., not "solve the system of equations for y" but rather "solve each individual equation so that it is y = mx + b").

First equation solved for y:

6x=5y+1
5y = 6x - 1
y = (6/5)x - 1/5

This equation defines a line with slope 6/5 and y-intercept -1/5.

Second equation solved for y:

-12x + 10y = 1
10y = 12x + 1
y = (12/10)x + 1/10
y = (6/5)x + 1/10

This equation defines a line with slope of 6/5 and y-intercept of 1/10

The two lines are parallel, because they have the same slope, 6/5. Since their y-intercepts are different, they do not intersect, and therefore there is no solution to the two equations treated as a system (as the first respondent found out).

If the slopes of the two lines had been negative reciprocals of each other (i.e., one is 6/5 and the other -5/6) the two lines would be perpendicular. Otherwise, if the slopes are not identical, and are not negative reciprocals, the answer is "neither parallel nor perpendicular."

Answer 2

Is this question to solve each of the equations for y? Given that you are then asked to determine if they are parallel, perpendicular or neither that would seem reasonable.

6x=5y+1
Subtract 1 from both sides and then divide both sides by 5 gives (6x-1)/5 = y or
y = (6/5)x+(1/5). Note that the slope of this line is (6/5) and the y-intercept is (0, 1/5)

-12x+10y=1
Add 12x to both sides then divided both sides by 10 gives (12x+1)/10 = y or y = ((6/5)x +(1/10) Note that the slope of this line is (6/5) and the y-intercept is (0, 1/10).

Since the two lines have the same slope but different y-intercepts the two lines are parallel.

Answer 3

Here's the best way to do this:

You know that 6x = 5y + 1

So break down the bottom equation like so:

(-2 * 6x) + 10y = 1

Then you can substitue for 6x.

(-2 *(5y+1)) + 10y = 1
(-10y - 2) + 10y = 1

By the looks of it there is no solution. Did you write the equations right?

Answer 4

they will intersect . and there is a unique solution