Coordinates of the vertices

Calculate the coordinates of the vertices of a triangle if the equations of its sides are
7x-4y-1 = 0
x-2y + 7 = 0
2x + y + 4 = 0

Correct answer:

x =  3
y =  5
a =  -3
b =  2
c =  -1
d =  -2

Step-by-step explanation:


7x-4y-1=0
x-2y+7=0

7·x-4·y-1=0
x-2·y+7=0

7x-4y = 1
x-2y = -7

Row 2 - 1/7 · Row 1 → Row 2
7x-4y = 1
-1.43y = -7.14


y = -7.14285714/-1.42857143 = 5
x = 1+4y/7 = 1+4 · 5/7 = 3

x = 3
y = 5

Our linear equations calculator calculates it.

a-2b+7=0
2a+b+4=0

a-2·b+7=0
2·a+b+4=0

a-2b = -7
2a+b = -4

Pivot: Row 1 ↔ Row 2
2a+b = -4
a-2b = -7

Row 2 - 1/2 · Row 1 → Row 2
2a+b = -4
-2.5b = -5


b = -5/-2.5 = 2
a = -4-b/2 = -4-2/2 = -3

a = -3
b = 2

Our linear equations calculator calculates it.

7c-4d-1=0
2c+d+4=0

7·c-4·d-1=0
2·c+d+4=0

7c-4d = 1
2c+d = -4

Row 2 - 2/7 · Row 1 → Row 2
7c-4d = 1
2.14d = -4.29


d = -4.28571429/2.14285714 = -2
c = 1+4d/7 = 1+4 · (-2)/7 = -1

c = -1
d = -2

Our linear equations calculator calculates it.



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