Question

# For what value of $$p$$ will the following pair of linear equations have infinitely many solutions:$$(p-3)x+3y=p$$$$px+py=12$$

Solution

## Given equation are$$(p-3)x+3y=p$$$$px+py=12$$The pair of linear equation has infinitely many solutions.$$\dfrac{a_1}{a_2}=\dfrac{b_1}{b_2}=\dfrac{c_1}{c_2}$$$$\dfrac{p-3}{p}=\dfrac{3}{p}=\dfrac{p}{12}$$$$\dfrac{a_1}{a_2}=\dfrac{c_1}{c_2}$$$$\dfrac{p-3}{p}=\dfrac{p}{12}$$$$(p-3)12=p^2$$$$12p-36=p^2$$$$p^2-12p-36=0$$$$p^2-6p-6p-36=0$$$$p(p-6)-6(p-6)=0$$$$p-6=0$$$$\therefore p=6$$.Mathematics

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