Find all solutions of the system?

Question

y + x^2 = 6x 
y + 6 x =36 


The solution or solutions of the system is: _____________

Answer 1

The system of equations are .

Step 1 : Solve the equation 2 : for y since the coefficient is 1.

Subtract 6x from each side.

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Step 2 : Substitute  for y in the equation 1 : to find the value of x.

Subtract 6x from each side.

Apply perfect square trinomial : .

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Step 3 : Substitute 6 for x in either equation to find y.

Equation 2 :

Subtract 36 from each side.

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The solution (x, y) = (6, 0).