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Which of the following pairs of linear equations are consistent/inconsistent? If consistent, obtain the solution graphically: (iii) 2x plus y minus 6 equals 0, 3x minus 2 y minus 4 equals 0

Q4.    Which of the following pairs of linear equations are consistent/inconsistent? If consistent, obtain the solution graphically:

                (iii)    2x + y - 6 =0, \qquad 4x - 2 y - 4 = 0

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Given, Equations,

\\2x + y - 6 =0, \qquad \\4x - 2 y - 4 = 0

Comparing these equations with  a_1x+b_1y+c_1=0\:and\:a_2x+b_2y+c_2=0, we get 

\\\frac{a_1}{a_2}=\frac{2}{4}=\frac{1}{2},\\\:\frac{b_1}{b_2}=\frac{1}{-2}=-\frac{1}{2}\:and\\\:\frac{c_1}{c_2}=\frac{-6}{-4}=\frac{3}{2}

As we can see 

\frac{a_1}{a_2}\neq\frac{b_1}{b_2}

It means the given equations have exactly one solution and thus pair of linear equations is consistent.

Now The points(x, y) satisfying the equation are,

X 0 2 3
Y 6 2 0

 

And The points(x,y) satisfying the equation \\4x - 2 y - 4 = 0 are,

X 0 1 2
Y -2 0 2

 

GRAPH:

As we can see both lines intersects at point (2,2) and hence the solution of both equation is x = 2 and y = 2.

 

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