Final answer:
To solve the system of equations x - y = 10 and x^2 + 4xy + y^2 = 52, we can use the substitution method. First, solve one equation for one variable and substitute it into the other equation. The solution set is the set of all ordered pairs that satisfy both equations.
Step-by-step explanation:
To solve the system of equations x - y = 10 and x2 + 4xy + y2 = 52, we can use the substitution method. First, solve one equation for one variable and substitute it into the other equation.
From the first equation, we can solve for x: x = y + 10.
Substitute this expression for x in the second equation: (y + 10)2 + 4(y + 10)y + y2 = 52. Simplify and solve the quadratic equation to find the possible values of y. Then substitute these values back into x = y + 10 to find the corresponding values of x.
The solution set for the equations is the set of all ordered pairs (x, y) that satisfy both equations.