The value of x and y in the given system of equation is 3.70 and 2.50 respectively.
A system of equations is a finite set of equations that can either be solved by using a substitution method or the elimination method.
From the given information:
[tex]\mathbf{x^2 + y^2 = 20}[/tex] ---- (1)
[tex]\mathbf{5^x + 4^y = 400}[/tex] ---- (2)
From equation (1), let's make (x) the subject of the formula and substitute the value of x into equation (2) to solve for y.
i.e.
[tex]\mathbf{x^2 + y^2 = 20}[/tex]
[tex]\mathbf{x^2 = 20- y^2}[/tex]
[tex]\mathbf{x = \sqrt{20- y^2}}[/tex] ---- (3)
Now, replace the value of x in equation (2), we have:
[tex]\mathbf{5^{ \sqrt{20- y^2}} + 4^y = 400}}[/tex]
solving for y;
y ≅ 2.50
Replacing the value of y in equation (3) to solve for (x), the value of x is:
[tex]\mathbf{x = \sqrt{20- 2.50^2}}[/tex]
x = 3.70
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