If the system of equations $$x+y+z=5$$, $$x+2y+3z=9$$ ,$$x+3y+$$α$$z=$$β has infinitely many solutions , then β−α equals

Question

If the system of equations   $$x+y+z=5$$,        $$x+2y+3z=9$$ ,$$x+3y+$$α$$z=$$β  has infinitely many solutions , then  β−α equals

Infinity Learn · Accepted Answer

Since, the system of equations has infinitely many solution, therefore $$D=D1$$−$$D2$$−$$D3=0Here$$,$$D=11112313$$α$$=1(2$$α−$$9)$$−$$1($$α−$$3)+1(3$$−$$2)=$$α−$$5$$ And $$D3=1$$    $$1$$    $$51$$    $$2$$    $$91$$    $$3$$    β$$=1(2$$β−$$27)$$−$$1($$β−$$9)+5(3$$−$$2)and$$ $$D3=11512913$$β$$=12$$β−$$27$$−$$1$$β−$$9+53$$−$$2=$$β−$$13$$ Now, $$D=0$$⇒   α−$$5=0$$  ⇒α$$=5$$ And  $$D3=0$$⇒β−$$13=0$$⇒β$$=13$$∴β−α$$=13$$−$$5=8$$

If the system of equations $x + y + z = 5, x + 2 y + 3 z = 9$ , $x + 3 y + α z = β$ has infinitely many solutions , then $β - α$ equals

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If the system of equations x+y+z=5, x+2y+3z=9 ,x+3y+αz=β has infinitely many solutions , then β−α equals

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If the system of equations $x + y + z = 5, x + 2 y + 3 z = 9$ , $x + 3 y + α z = β$ has infinitely many solutions , then $β - α$ equals