# Coordinates

Determine the coordinates of the vertices and the area of the parallelogram, the two sides of which lie on the lines 8x + 3y + 1 = 0, 2x + y-1 = 0 and the diagonal on the line 3x + 2y + 3 = 0

x0 =  -2
y0 =  5
x1 =  1
y1 =  -3
x2 =  5
y2 =  -9
x3 =  8
y3 =  -17
S =  14

### Step-by-step explanation:

8x0+3y0+1=0
2x0+y0-1=0

8·x0+3·y0+1=0
2·x0+y0-1=0

8x0+3y0 = -1
2x0+y0 = 1

Row 2 - 2/8 · Row 1 → Row 2
8x0+3y0 = -1
0.25y0 = 1.25

y0 = 1.25/0.25 = 5
x0 = -1-3y0/8 = -1-3 · 5/8 = -2

x0 = -2
y0 = 5

Our linear equations calculator calculates it.

8x1+3y1+1=0
3x1+ 2y1+3=0

8·x1+3·y1+1=0
3·x1+ 2·y1+3=0

8x1+3y1 = -1
3x1+2y1 = -3

Row 2 - 3/8 · Row 1 → Row 2
8x1+3y1 = -1
0.88y1 = -2.63

y1 = -2.625/0.875 = -3
x1 = -1-3y1/8 = -1-3 · (-3)/8 = 1

x1 = 1
y1 = -3

Our linear equations calculator calculates it.

2x2+y2-1=0
3x2+ 2y2+3=0

2·x2+y2-1=0
3·x2+ 2·y2+3=0

2x2+y2 = 1
3x2+2y2 = -3

Pivot: Row 1 ↔ Row 2
3x2+2y2 = -3
2x2+y2 = 1

Row 2 - 2/3 · Row 1 → Row 2
3x2+2y2 = -3
-0.33y2 = 3

y2 = 3/-0.33333333 = -9
x2 = -3-2y2/3 = -3-2 · (-9)/3 = 5

x2 = 5
y2 = -9

Our linear equations calculator calculates it. Did you find an error or inaccuracy? Feel free to write us. Thank you!

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