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what is the solution set of y equals x squared plus 2X + 7 + y equals x + 7

Sagot :

The given equations are

y = x^2 + 2x + 7

y = x + 7

We would substitute y = x + 7 into the first equation. It becomes

x + 7 = x^2 + 2x + 7

Collecting like terms, it becomes

x^2 + 2x - x + 7 - 7 = 0

x^2 + x = 0

By factorising x, it becomes

x(x + 1) = 0

Thus,

x = 0 or x + 1 = 0

x = 0 or x = - 1

Substituting x = 0 into y = x + 7, it becomes

y = 0 + 7

y = 7

Thus, one solution set is (0, 7)

Substituting x = - 1 into y = x + 7, it becomes

y = - 1 + 7

y = 6

Thus, another solution set is (- 1, 6)

Therefore, the solution sets are

{(0, 7), (- 1, 6)}

Option A is correct

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