Question

the system of equations 2x+3y=5,,,6x+9y=k have infinite many solutions the then value of k​

Answer 1

Answer:

Since it has infinitely many solution.

so, a1/a2=b1/b2=c1/c2

here a1=2,b1=3 and c1=5 and a2=6, b2=9,c2=k.

now we get 2/6=3/9=5/k.

so 3/9=5/k.

45=3k

k=45/3k=15.

so the value of k is 15

Answer 2

Answer:

For the infinite solutions the value of k is 15 for the given equations.

Step-by-step explanation:

• Infinite solutions are the solutions whenthere are a lot number of solutions for the equations and the their number cant be known.

• The equations have infinite solutions if

      $\frac{a_{1} }{a_{2}} =\frac{b_{1}}{b_{2}} =\frac{c_{1}}{c_{2}}$

• For the given equation

        $2x+3y=5$

        $a_{1}=2,\ \ \ b_{1}=3\ \ \ c_{1}=6$

• For the given equation

        $6x+9y=k$

        $a_{2}=6,\ \ \ b_{1}=9\ \ \ c_{1}=k$

• since equation have infinite solution, following comdition holds

         $\frac{a_{1} }{a_{2}} =\frac{b_{1}}{b_{2}} =\frac{c_{1}}{c_{2}}$  

         $\frac{2 }{6} =\frac{3}{9} =\frac{5}{k}$

         $\frac{3}{9} =\frac{5}{k}\\3k=45\\k=15$

Conclusion:

The system of equations   $2x+3y=5$and    $6x+9y=k$ have infinite many solutions the then value k is 15