Question

The lines 2x - 3y = 1 and 2x + 3y = 2 are intersecting. true or false

Answer 1

2x - 3y = 1
-3y = -2x + 1
y = 2/3x - 1/3...slope = 2/3, y int = -1/3

2x + 3y = 2
3y = -2x + 2
y = -2/3x + 2/3...slope = -2/3, y int = 2/3

different slopes, different y int's....means 1 solution...so yes, they intersect
TRUE

Answer 2

the given statement is true.

Explanation:

The given lines are

2x - 3y = 1 and 2x + 3y = 2

Write these equations in slope intercept form of a line y = mx +b

For the first equation

`2x-3y=1\\\\3y=2x-1\\\\y=(2)/(3)x-(1)/(3)`

For the first equation

`2x+3y=2\\\\3y=-2x+2\\\\y=-(2)/(3)x+(2)/(3)`

The slope and y-intercepts of first line are 2/3 and -1/3 respectively.

The slope and y-intercepts of second line are -2/3 and 2/3 respectively.

Since, the slopes and y-intercepts of these lines are different.

Hence, these lines are intersecting.

Therefore, the given statement is true.