please solve question no.22 and 23
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a eqution has infinite solutions if coefficient of x ratio= coefficient of y ratio
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- Question⇒ Find c if the system of equations cx + 3y + (3-c) = 0 and 12x + cy -c = 0 has infinitely many solutions?
Step-by-step explanation:
- Given: System of Equations cx + 3y + ( 3 - c ) = 0 and 12x + cy - c = 0
- To find: Value of c if system of equation has infinitely many solution
- If system of equation are a1x+b1y+c1=0 and a2x+b2y+c2=0
- & they have infinitely many solution then it satisfy the following condition,
- a1/a2=b1/b2=c1/c2
- From given system of equation.
- a1=c ,b1=3 ,c1=3-c and a2= 12 , b2=c ,c2= -c
- putting these value in condition of infinitely many solution we get,
- c/12=3/c=3-c/-c
- Equating 2 at a time we get,
- c/12=3/c
- c*c=12*3
- c^=36
- c=±√36
- c=±6
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