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  • Graphically, solve the following pair of equations: 2x + y = 6 2x – y + 2 = 0 Find the ratio of the areas of the two triangles formed by the lines representing these equations with the x-axis and the lines with the y-axis.

Graphically, solve the following pair of equations:2x + y = 6 and  2x – y + 2 = 0 Find the ratio of the areas of the two triangles formed by the lines representing these equations with the x-axis and the lines with the y-axis.

Answers (1)

Solution:
Here the equations are 2x + y = 6, 2x – y = –2
2x + y = 6

x 0 3
y 6 0

2x – y = –2

x 0 -1
y 2 0

In the graph, we find that the lines intersect at (1, 4) Hence x = 1, y = 4 is the solution of the equations. The two triangles are ABC and DBE.
Area of \bigtriangleupABE = \frac{1}{2} × Base × perpendicular

  = \frac{1}{2}\times 4\times 4= 8
Area of \bigtriangleupADC = \frac{1}{2} × Base × perpendicular

  = \frac{1}{2}\times 4\times 1

= 2
\bigtriangleupABE area: \bigtriangleupADC Area
4: 1

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infoexpert27

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