Respuesta :
Answer:
(- 1, 4 ) and (2, 7 )
Step-by-step explanation:
y = x² + 3 → (1)
y = x + 5 → (2)
substitute y = x² + 3 into (2)
x² + 3 = x + 5 ( subtract x + 5 from both sides )
x² - x - 2 = 0
(x - 2(x + 1) = 0
equate each factor to zero and solve for x
x - 2 = 0 ⇒ x = 2
x + 1 = 0 ⇒ x = - 1
substitute these values into (2) for corresponding values of y
x = - 1 : y = - 1 + 5 = 4 ⇒ (- 1, 4 )
x = 2 : y = 2 + 5 = 7 ⇒ (2, 7 )
Answer:
(x1, y1) = (-1, 4)
(x2, y2) = (2, 7)
Step-by-step explanation:
y = x2 + 3
y = x + 5
substitute the given value of y into the equation y=x+5
x^2 + 3 = x + 5
solve the equation for x
x = -1
x = 2
substitute the given value of x into the equation y=x+5
y = -1 + 5
x = 2
solve the equation for y
y = 4 ----> y = 4
y = 2 + 5 ----> y = 7
the possible solutions of the system are the ordered pairs (x,y)
(x1, y1) = (-1, 4)
(x2, y2) = (2, 7)
check if the given ordered pairs are the solutions of the system of equations
4 = (-1)^2 + 3 7 = 2^2 + 3
4 = -1 + 5 7 = 2 + 5
simplify the equalities
4 = 4 7 = 7
4 = 4 7 = 7
since all of the equalities are true, the ordered pairs are the solutions of the system
(x1, y1) = (-1, 4)
(x2, y2) = (2, 7)
