in MMA : how to get the variable values by solving one equation directly?

In Mathematica, I want to get the variable values by solving one equation directly, this means: I have the equation
$a_1 x + b_1 y + c_1 = d_1 \\ a_2 x + b_2 y + c_2 = d_2$a1​x+b1​y+c1​=d1​a2​x+b2​y+c2​=d2​
if we finally want to get the value $A x^2 + B y^2$Ax2+By2, we need to solve the above equation firstly to get $x,y$x,y, so in Mathematica

but now we directly compute the $A x^2 + B y^2$Ax2+By2,
so we can see that it doesn’t do anything (our aim is to substitute $x,y$x,y into $A x^2 + B y^2$Ax2+By2).

Now we give the solution