Final answer:
To solve the system x + y = 11 and y = 3x² - 22x + 41, substitute the quadratic into the linear equation, solve the resulting quadratic for x, and finally solve for y.
Step-by-step explanation:
The question involves solving a system of equations in which y is defined both as a linear combination of x and as a quadratic expression in terms of x. To solve for the solutions to the system x + y = 11 and y = 3x² - 22x + 41, we can substitute the quadratic expression in place of y in the first equation and then solve for x.
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- Substitute y from the second equation into the first equation: x + (3x² - 22x + 41) = 11.
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- Simplify the equation and solve the resulting quadratic equation for x.
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- Once x is found, substitute back into either equation to find the corresponding y values.
This is a typical algebraic procedure to solve systems of equations where one equation is linear, and the other is quadratic.
The complete questiojn is: Which of the following is a solution to the system be x+y=11 y=3x²-22x+41 is: