A) A unique solution \[x=1,\,\,y=1\]
B) A unique solution \[x=0,\,\,y=4\]
C) No solution
D) Infinite solutions
Correct Answer: D
Solution :
(d):Given equations of system \[2x+y=2\] \[4x+2y=4\] \[\text{Here,}\,{{a}_{1}}=2,{{b}_{1}}=1\,\,\text{and}\,{{c}_{1}}=2\] \[and\,{{a}_{1}}=4,{{b}_{2}}=2\,and\text{ }{{c}_{3}}=4\] \[\therefore \frac{{{a}_{1}}}{{{a}_{2}}}=\frac{{{b}_{1}}}{{{b}_{2}}}=\frac{{{c}_{1}}}{{{c}_{2}}}=\frac{1}{2}\] So, the system of equation has infinite solutions because it is a coincident line.
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