MATH SOLVE

2 months ago

Q:
# Which ordered pair is a solution to the system of equations y=x+3 and y=x^2-x

Accepted Solution

A:

For this case we have the following system of equations:[tex]y = x + 3\\y = x ^ 2-x[/tex]Equating the equations we have:[tex]x ^ 2-x = x + 3\\x ^ 2-x-x-3 = 0\\x ^ 2-2x-3 = 0[/tex]To find the solutions we factor the equation. To do this, we look for two numbers that, when multiplied, result in -3 and when added, result in -2.These numbers are: -3 and +1[tex]-3 + 1 = -2\\-3 * (+ 1) = - 3[/tex]Thus, the factored equation is:[tex](x-3) (x + 1) = 0[/tex]Then, the solutions for the variable "x" are:[tex]x_ {1} = 3\\x_ {2} = - 1[/tex]We find the solutions for the variable "y":[tex]y_ {1} = x_ {1} + 3 = 3 + 3 = 6\\y_ {2} = x_ {2} + 3 = -1 + 3 = 2[/tex]Thus, the solutions are:[tex](x_ {1}, y_ {1}): (3,6)\\(x_ {2}, y_ {2}): (-1,2)[/tex]ANswer:[tex](x_ {1}, y_ {1}): (3,6)\\(x_ {2}, y_ {2}): (-1,2)[/tex]