Question

Solve the system of equations

x+y=15
Y=x^(2)-5

(-5,20) and (4,11)
(3,4) and (7,8)
(5,10) and (-4,19)
(5,20) and (4,11)

Answer 1

(a) (-5,20) and (4,11)

Explanation:

You want the solutions to the system of equations ...

• x + y = 15
• y = x² - 5

Substitution

Using the second equation to substitute for y in the firs equation, we have ...

x +x² -5 = 15

x² +x -20 = 0 . . . . . subtract 15, put in standard form

(x +5)(x -4) = 0 . . . . . factor

Zero product rule

A product is zero only when one or more factors is zero. The values of x that make the factors zero are ...

x = -5 and x = 4

The corresponding values of y are ...

y = 15 -x

y = 15 -{-5, 4} = {20, 11}

The solutions are (x, y) = (-5, 20) and (4, 11).