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y = x2 - 4x + 4
y = 4 - x
If the ordered pair (x, y) satisfies the system of equations above, what is one possible value of x ?
  • a)
    0
  • b)
    3
  • c)
    both of these
  • d)
    None of these
Correct answer is option 'C'. Can you explain this answer?
Most Upvoted Answer
y = x2 - 4x + 4y = 4 - xIf the ordered pair (x, y) satisfies the syste...
To find a possible value for x that satisfies the given system of equations, we need to solve the equations simultaneously. Let's solve them step-by-step:

1. Start with the first equation: y = x^2 - 4x.

2. Substitute this expression for y into the second equation: 4(x^2 - 4x) = 4 - x.

3. Simplify the equation: 4x^2 - 16x = 4 - x.

4. Rearrange the equation to get a quadratic equation: 4x^2 - 15x - 4 = 0.

5. To factorize the quadratic equation, find two numbers that multiply to give -16 and add up to -15. The numbers are -16 and 1, so the factored form of the equation is: (4x + 1)(x - 4) = 0.

6. Set each factor equal to zero and solve for x:
4x + 1 = 0 or x - 4 = 0.

7. Solve the first equation: 4x + 1 = 0.
Subtract 1 from both sides: 4x = -1.
Divide by 4: x = -1/4.

8. Solve the second equation: x - 4 = 0.
Add 4 to both sides: x = 4.

9. Therefore, the possible values of x that satisfy the system of equations are -1/4 and 4.

Hence, the correct answer is option C: both of these.
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Community Answer
y = x2 - 4x + 4y = 4 - xIf the ordered pair (x, y) satisfies the syste...
The correct answer is 0 or 3. For an ordered pair to satisfy a system of equations, both the x- and y-values of the ordered pair must satisfy each equation in the system. Both expressions on the right-hand side of the given equations are equal to y, therefore it follows that both expressions on the right-hand side of the equations are equal to each other: x2 − 4x + 4 = 4 − x. This equation can be rewritten as x2 − 3x = 0, and then through factoring, the equation becomes x(x − 3) = 0. Because the product of the two factors is equal to 0, it can be concluded that either x = 0 or x – 3 = 0, or rather, x = 0 or x = 3.
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