Question

X+y=2 8x+3y=-19 substitution

Answer 1

Input:

f(x, y) = x^2 - y^2

Geometric figure:

hyperbolic paraboloid

3D plot:

3D plot

Contour plot:

Contour plot

Alternate form:

f(x, y) = (x - y) (x + y)

Alternate form assuming x and y are positive:

x^2 = f(x, y) + y^2

Properties as a function:

Domain

R^2

Range

R (all real numbers)

Parity

even

Partial derivatives:

d/dx(x^2 - y^2) = 2 x

d/dy(x^2 - y^2) = -2 y

Indefinite integral assuming all variables are real:

integral(x^2 - y^2) dx = x^3/3 - x y^2 + constant

Answer 2

{x,y}={−5,−7}

Explain:

// Solve equation [2] for the variable y [2] 3y = 7x + 14 [2] y = 7x/3 + 14/3 // Plug this in for variable y in equation [1] [1] 8x - 3•(7x/3+14/3) = -19 [1] x = -5 // Solve equation [1] for the variable x [1] x = - 5 // By now we know this much : x = -5 y = 7x/3+14/3 // Use the x value to solve for y y = (7/3)(-5)+14/3 = -7 Solution : {x,y} = {-5,-7}

Hoped I helped