What is the point of intersection of the lines x-2y-11=0 and 4x-y-20=0 ?

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We'll re-write the 1st equation of the line, moving 11 to the right side:

x - 2y = 11 (1)

We'll re-write the 2nd equation of the line, moving 20 to the right side:

4x - y = 20 (2)

We'll multiply (2) by -2:

-8x + 2y = -40 (3)

We'll add (3) to (1):

x - 2y - 8x + 2y = 11 - 40

We'll combine and eliminate like terms:

-7x = -29

x = 29/7

29/7 - 2y = 11

-2y = 11 - 29/7

-2y = (77-29)/7

y = -27/7

**The coordinates of the intercepting point of the lines are (29/7 ; -27/7).**

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