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Which of the following pairs of linear equations are consistent/inconsistent? If consistent, obtain the solution graphically: (i) x + y = 5, 2x + 2y = 10

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

                    (i)    x + y = 5 \qquad 2x + 2 y = 10

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Given, Equations,

\\x + y = 5 \qquad\\ 2x + 2 y = 10

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{1}{2},\\\:\frac{b_1}{b_2}=\frac{1}{2}\:and\\\:\frac{c_1}{c_2}=\frac{5}{10}=\frac{1}{2}

As we can see 

\frac{a_1}{a_2}=\frac{b_1}{b_2}=\frac{c_1}{c_2}

It means the given equations have an infinite number of solutions and thus pair of linear equations is consistent.

The points (x,y) which satisfies in both equations are 

X 1 3 5
Y 4 2 0

Graph.

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