Question

Lucy says that the solution to the system y = x^2 + 3x - 6 and y = -x - 1 is (-5,1). Do you agree or disagree? Answer the question and use evidence from solving the system to support your answer step by step.

A) Agree, by solving the system step by step, the solution is (-5,1).
B) Disagree, the solution is (-4,3) by solving the system step by step.
C) Agree, no need to solve; Lucy is correct.
D) Disagree, the solution is (-3,2) by solving the system step by step.

Answer 1

Lucy's solution to the system of equations is incorrect. The correct solution is (-5, -2) or (1, -2).

Step-by-step explanation:

Lucy's solution to the system of equations can be checked by substituting the given values of x and y into the equations. The system of equations is:

y = x^2 + 3x - 6

y = -x - 1

Substituting x = -5 and y = 1 into the first equation:

1 = (-5)^2 + 3(-5) - 6

1 = 25 - 15 - 6

1 = 4 - 6

1 = -2

As the left side of the equation is not equal to the right side, Lucy's solution of (-5,1) is incorrect. Therefore, I disagree with Lucy's solution.

The correct solution to the system of equations can be found by setting the two equations equal to each other and solving for x:

x^2 + 3x - 6 = -x - 1

Bringing all terms to one side:

x^2 + 4x - 5 = 0

Factoring the equation:

(x - 1)(x + 5) = 0

Setting each factor equal to zero:

x - 1 = 0 or x + 5 = 0

x = 1 or x = -5

Substituting the values of x back into either equation to solve for y:

If x = 1, y = 1^2 + 3(1) - 6 = -2

If x = -5, y = (-5)^2 + 3(-5) - 6 = -2

Therefore, the correct solution to the system of equations is (-5, -2) or (1, -2).