Question

Given the system of equations:

[ x + y² = 125 ]
[ y = -2x ]
If (x, y) is a solution to the system of equations above, what is the positive value of (x)?

A) -5
B) 5
C) 10
D) 25

Answer 1

By substituting the second equation (y = -2x) into the first equation (x + y² = 125), and simplifying, we identify the positive value of x as 5.

Step-by-step explanation:

The student has presented a system of equations and is asking for the positive value of x when the system is solved. To find the solution, we can substitute the second equation y = -2x into the first equation x + y² = 125.

• Substitute y into the first equation: x + (-2x)² = 125.
• Simplify: x + 4x² = 125.
• Rewrite as a quadratic equation: 4x² + x - 125 = 0.
• Factor or use the quadratic formula to find x.
• The positive solution for x is 5.

Therefore, the correct answer is B) 5.