Given the coincidental lines mx+3y+2=0 and 2x+ny-8=0 what are m and n ?

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hala718's profile pic

hala718 | High School Teacher | (Level 1) Educator Emeritus

Posted on

Given the lines:

mx + 3y + 2 = 0

2x + ny -8 - 0

Given that both lines are coincidental.

Then the equations of the lines must be the same.

==> Then the rations should be equal.

==< m/2 = 3/n = 2/-8

Now we will solve each variable.

==?> m/2 = 2/-8 = -1/4

==> 4m= -2 ==? m = -2/4 = -1/2

Now we will solve for n.

==> 3/n = 2/-8 = -1/4

==> -n = 12 ==> n= -12

Then the values are: m= -1/2  and n= -12

giorgiana1976's profile pic

giorgiana1976 | College Teacher | (Level 3) Valedictorian

Posted on

If 2 lines are coincidental then the following relation is true:

m/2 = 3/n = 2/-8

We'll take the first and the last fractions:

m/2 = 1/-4

-4m = 2

m = -1/2

We'll take the 2nd and the last fractions:

3/n = 1/-4

n = -12

The coefficients m and n of the coincidental lines are: m = -1/2 and n = -12.

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