Answer:
(0, 4 ) and ( [tex]\frac{1}{2}[/tex], [tex]\frac{13}{2}[/tex] )
Step-by-step explanation:
Given the2 equations
y = 4x² + 3x + 4 → (1)
y = 5x + 4 → (2)
Substitute y = 4x² + 3x + 4 into (2)
4x² + 3x + 4 = 5x + 4 ( subtract 5x + 4 from both sides )
4x² - 2x = 0 ← factor out 2x from each term
2x(2x - 1) = 0
Equate each factor to zero and solve for x
2x = 0 ⇒ x = 0
2x - 1 = 0 ⇒ 2x = 1 ⇒ x = [tex]\frac{1}{2}[/tex]
Substitute these values into (2) for corresponding values of y
x = 0 : y = 5(0) + 4 = 0 + 4 = 4 ⇒ (0, 4 )
x = [tex]\frac{1}{2}[/tex] : y = [tex]\frac{5}{2}[/tex] + 4 = [tex]\frac{13}{2}[/tex] ⇒ ([tex]\frac{1}{2}[/tex], [tex]\frac{13}{2}[/tex] )
