Question

Which steps could be part of the process in algebraically solving the system of equations, y + 5x = x2 + 10 and y = 4x –

10? Select two options.
Oy = x2 + 5x + 10
Oy + 5x = x2 + 10 + 4x – 10
0 0 = x2 - 9x
0 0 = x2 - 9x + 20
One x-value of a solution to the system is 4.

Answer 1

To algebraically solve the system of equations y + 5x = x2 + 10 and y = 4x – 10, you can follow these steps: Rewrite the equations, substitute one equation into the other, simplify the equation, factor the quadratic equation, set each factor equal to zero, and solve for x.

Step-by-step explanation:

1. Rewrite the first equation in standard form: x^2 + 5x - y + 10 = 0
2. Substitute the value of y from the second equation into the first equation: x^2 + 5x - (4x - 10) + 10 = 0
3. Simplify the equation: x^2 + x - 20 = 0
4. Factor the quadratic equation: (x - 4)(x + 5) = 0
5. Set each factor equal to zero and solve for x: x - 4 = 0 or x + 5 = 0
6. You find two possible values for x: x = 4 or x = -5