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  • Find the values of p and q for which the following system of equations has infinite number of solutions: 2x+3y=7 (p+q)x+(2p?q)y=21

Find the values of p and q for which the following system of equations has infinite number of solutions: 2x+3y=7 (p+q)x+(2p?q)y=21

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This;system;of;equation;is;of;the;form\* a_1x+b_1y=c_1\*a_2 x+b_2y=c_2\*where;a_1=2,;b_1=3,;c_1=7 \* and,;a_2=p+q,;b_2=2p-q;and;c_2=21\* For;infinitely;many;solutions,; we;must;have,\* fraca_1b_1=fraca_2b_2=fracc_1c_2\* The;given;system;of;equations ;will ;have ;infinite ;number ;of ;solutions,;if\* Rightarrow frac2p+q=frac32p-q=frac321=frac13\* Rightarrow frac2p+q=frac13Rightarrow p+q=6;;;..eq(1)\* Rightarrow frac32p-q=frac13Rightarrow 2p-q=9;;;..eq(2)\* From;..eq(1); and;..eq(2),;we;get.\* p=15;and;q=1

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Deependra Verma

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