Determine whether the two lines 2x 4y 3 and x 2y 7 are i

Determine whether the two lines 2x + 4y = 3 and x - 2y = 7 are intersecting, parallel, or coincident.

2x+4y = 3

x - 2y = 7

Two lines are parallel if the ration of coeffieicents of x and y are equal and this ratio is not equal to ratio of constants.

here we have coeff of x ratio = 2/1 , coefficient of y ratio = 4/-2 = -2/1 coeffieicent of constant = 3/7

here the three ratios are not equal So the lines are neither parallel, nor coincidental.

let us use elimination to solve it.

2x+4y = 3

2x-4y = 14 (multiplied eq 2 by 2)

Adding above 2 equations

4x = 17, so x = 17/4

y = 9/2.

So the given lines are intersecting.