Question

Solve each of the following system of equations graphically and find the vertices and area of the triangle formed by the lines and the x-axis: 2x-3y+4=0 4x-3y+4=0

Answer 1

Answer:

2x−3y+4=0....(1)

x+2y−5=0......(2)

Isolate x from equation (1) and find the value of x and y.

2x−3y+4=0

or x=(3y−4)/2

x y

−2 0

1 2

4 4

Similarly, isolate x from equation (2) and find the values of x and y.

x+2y−5=0

or x=5−2y

x y

5 0

3 1

1 2

Graph:

Now,

Find the area of triangle BAD:

Area of △BAD=1/2(base×altitude)

=1/2×7×2

=7 sq.units.

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Answer 2

Answer:

2x−3y+4=0....(1)

x+2y−5=0......(2)

Isolate x from equation (1) and find the value of x and y.

2x−3y+4=0

or x=(3y−4)/2

x y

−2 0

1 2

4 4

Similarly, isolate x from equation (2) and find the values of x and y.

x+2y−5=0

or x=5−2y

x y

5 0

3 1

1 2

Graph:

Now,

Find the area of triangle BAD:

Area of △BAD=1/2(base×altitude)

=1/2×7×2

=7 sq.units.

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