Answer:
Explanation:
To solve the system of equations, y + 5x = x^2 + 10 and y = 4x - 10 algebraically, the following steps could be used:
Substitute y = 4x - 10 from the second equation into the first equation, to get:
4x - 10 + 5x = x^2 + 10
Simplify the left side of the equation by combining like terms, to get:
9x - 10 = x^2 + 10
Move all terms to one side of the equation, to get:
x^2 - 9x + 20 = 0
Factor the quadratic equation to get:
(x - 4)(x - 5) = 0
Use the zero product property to find the x-values of the solutions, which are x = 4 and x = 5.
Substitute each x-value back into one of the original equations to find the corresponding y-value. For example, when x = 4:
y = 4(4) - 10 = 6
Write the solution as an ordered pair (x, y). The solutions to the system of equations are (4, 6) and (5, 10).
Therefore, the correct steps that could be part of the process to solve the system of equations are:
Substitute y = 4x - 10 from the second equation into the first equation, to get:
4x - 10 + 5x = x^2 + 10
Simplify the left side of the equation by combining like terms, to get:
9x - 10 = x^2 + 10
Move all terms to one side of the equation, to get:
x^2 - 9x + 20 = 0
Factor the quadratic equation to get:
(x - 4)(x - 5) = 0
Use the zero product property to find the x-values of the solutions, which are x = 4 and x = 5.
Substitute each x-value back into one of the original equations to find the corresponding y-value. For example, when x = 4:
y = 4(4) - 10 = 6
Write the solution as an ordered pair (x, y). The solutions to the system of equations are (4, 6) and (5, 10).
So, the correct options are:
Substitute y = 4x - 10 from the second equation into the first equation, to get:
4x - 10 + 5x = x^2 + 10
Simplify the left side of the equation by combining like terms, to get:
9x - 10 = x^2 + 10
Move all terms to one side of the equation, to get:
x^2 - 9x + 20 = 0
Factor the quadratic equation to get:
(x - 4)(x - 5) = 0
Use the zero product property to find the x-values of the solutions, which are x = 4 and x = 5.