Answer:
2 solutions
Step-by-step explanation:
y = - 2x + 3 → (1)
y = x² - 6x + 3 → (2)
substitute y = x² - 6x + 3 into (1)
x² - 6x + 3 = - 2x + 3 ( subtract - 2x + 3 from both sides )
x² - 4x = 0 ← factor out x from each term on the left side
x(x - 4) = 0
equate each factor to zero and solve for x
x = 0
x - 4 = 0 ⇒ x = 4
substitute these values into (1)
x = 0 : y = - 2(0) + 3 = 0 + 3 = 3 ⇒ (0, 3 )
x = 4 : y = - 2(4) + 3 = - 8 + 3 = - 5 ⇒ (4, - 5 )
the 2 solutions are (0, 3 ) and (4, - 5 )
