Question

If x=7 and y =3 is the solution of equations ax + by =18 and bx + ay =12 then a+b = _________
(-7,-3,3,7)​

Answer 1

Answer:

ans is a=9/4,b=3/4.....so a+b=3...ans is 3

Answer 2

Answer :

• a + b = 3

Step-by-step explanation :

Given,

=> equations,

• ax + by = 18
• bx + ay = 12

=> x = 7 , y = 3 is the solution

To find,

a + b = ?

Solution,

 Substitute x = 7, y = 3 in both the equations,

• ax + by = 18

         a(7) + b(3) = 18

          7a + 3b = 18

           7a = 18 - 3b

            a = (18 - 3b)/7

         

• bx + ay = 12

        b(7) + a(3) = 12

         7b + 3a = 12

 substitute the value of a

         $7b+3(\frac{18-3b}{7})=12 \\\\\\ 7b+\frac{54-9b}{7} =12 \\\\\\ \frac{49b+54-9b}{7} =12 \\\\\\ 40b+54=12\times 7 \\\\\\\ 40b+54=84 \\\\ \\ 40b=84-54 \\\\\\ 40b=30 \\\\\\ \bf \implies b=\frac{3}{4}$

____________________________

        $a=\frac{18-3b}{7} \\\\\\ a=\frac{18-3(\frac{3}{4})}{7} \\\\\\ a=\frac{18-\frac{9}{4}}{7} \\\\\\ a=\frac{\frac{72-9}{4}}{7} \\\\\\ a=\frac{63}{28} \\\\\\ \bf a=\frac{9}{4}$

_______________________________

=> a + b

        $=\frac{9}{4} +\frac{3}{4} \\\\ =\frac{12}{4} \\\\ =3$

∴ a + b = 3