Question

Consider the following system of equations: 10 + y = 5x + x² and 5x + y = 1. What are the solutions to the system? (, -4) and (, ___).

Answer 1

The solutions to the system of equations are (3, -14) and (-3, 16). This is obtained by expressing y from one equation, substituting it into another, and solving for x and y.

Step-by-step explanation:

The student asked for the solution to a system of equations:

• 10 + y = 5x + x²
• 5x + y = 1

To solve the system, we can start by expressing y from the second equation:

• y = 1 - 5x

Substitute this expression for y into the first equation:

• 10 + (1 - 5x) = 5x + x²

Now, we combine like terms and set the equation to zero to find the values of x:

• x² + 5x - 5x + 1 - 10 = 0
• x² - 9 = 0

Solving for x:

1. x = 3
2. x = -3

Substitute x back into y = 1 - 5x to find corresponding y values:

1. For x = 3, y = 1 - 5(3) = -14
2. For x = -3, y = 1 - 5(-3) = 16

Therefore, the solutions are (3, -14) and (-3, 16).