Answer:
68
Step-by-step explanation:
[tex]\textsf{Equation 1}:\:x-5=y[/tex]
[tex]\textsf{Equation 2}:\:xy+4=0[/tex]
Substitute Equation 1 into Equation 2:
[tex]\implies x(x-5)+4=0[/tex]
[tex]\implies x^2-5x+4=0[/tex]
Factorize:
[tex]\implies (x-1)(x-4)=0[/tex]
Therefore:
[tex]x=1, x=4[/tex]
Substitute found values of [tex]x[/tex] into Equation 1 and solve for [tex]y[/tex]:
[tex]x=1\implies 1-5=-4[/tex]
[tex]x=4\implies 4-5=-1[/tex]
Substitute found values into [tex]4x^2+4y^2[/tex] and solve:
[tex]\textsf{For}\:(1,-4)\implies 4(1)^2+4(-4)^2=68[/tex]
[tex]\textsf{For}\:(4,-1)\implies 4(4)^2+4(-1)^2=68[/tex]
Note: As [tex]4x^2+4y^2[/tex], the values of x and y can be interchanged, so no need to input both sets of ordered pairs into the equation to solve.
