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Find the solution(s) to the system of equations. Select all that apply.

WA
y = x² - 4
y=-2x - 5

1 Answer

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Final answer:

To solve the system of equations, substitute the linear equation into the quadratic, solve for x, and then back-substitute to find y, ensuring to carefully follow algebraic steps and check the solutions.

Step-by-step explanation:

Finding Solutions to a System of Equations

To find the solution(s) to the system of equations, you must first recognize the equations involved. The system provided is comprised of a quadratic equation WAy = x² - 4 and a linear equation y = -2x - 5. To solve, you substitute the linear equation into the quadratic equation and solve for x:

  • Replace y in the first equation with -2x - 5: WA(-2x - 5) = x² - 4
  • Open the parenthesis: -2WAx - WA5 = x² - 4
  • Rearrange the equation: x² - 4 + 2WAx + WA5 = 0
  • Factor the quadratic equation or use the quadratic formula to find the values of x.
  • Substitute the found values of x back into y = -2x - 5 to get the corresponding y values.

This problem requires careful algebraic steps and checking to ensure that all possible solutions are found. Both equations must hold true for each solution to the system.

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