What are the solutions to the system?
y = x2 – 6x + 7
y = –x + 13
A. (–1, 14) and (6, 7)
B. (–1, 7) and (6, 14)
C. (–1, 13) and (6, 7)
D. no solution
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Apologies for the confusion. The system of equations given is:
y = x^2 - 6x + 7
y = -x + 13
To find the solutions, we can set the two equations equal to each other:
x^2 - 6x + 7 = -x + 13
Simplifying this equation gives:
x^2 - 5x - 6 = 0
Factoring this equation gives:
(x - 6)(x + 1) = 0
Therefore, the solutions are x = -1 and x = 6.
To find the corresponding y-values, we can substitute these values of x back into either of the original equations. Using the second equation:
y = -x + 13
When x = -1, y = -(-1) + 13 = 14.
When x = 6, y = -(6) + 13 = 7.
Therefore, the solutions to the system are (-1, 14) and (6, 7), which is answer choice A.
y = x^2 - 6x + 7
y = -x + 13
To find the solutions, we can set the two equations equal to each other:
x^2 - 6x + 7 = -x + 13
Simplifying this equation gives:
x^2 - 5x - 6 = 0
Factoring this equation gives:
(x - 6)(x + 1) = 0
Therefore, the solutions are x = -1 and x = 6.
To find the corresponding y-values, we can substitute these values of x back into either of the original equations. Using the second equation:
y = -x + 13
When x = -1, y = -(-1) + 13 = 14.
When x = 6, y = -(6) + 13 = 7.
Therefore, the solutions to the system are (-1, 14) and (6, 7), which is answer choice A.