Question

How many real solutions does this system of equations have? y=x^2+3x+4
y−x=7

Answer 1

The system of equations has two real roots

Step-by-step explanation:

y = x² + 3x + 4 ------------(I)

y - x = 7 ------------------------(II)

y = 7 +x

Substitute y = 7 + x in equation (I),

7 + x = x² + 3x + 4

0 = x² + 3x + 4 - x - 7

0 = x² + 3x - x + 4 - 7

Combine like terms,

0 = x² + 2x - 3

x² + 2x - 3 = 0

a = 1; b = 2; c = -3

Discriminant = b² - 4ac

= 2² - 4*1*(-3)

= 4 + 12

= 16

System of equations has two real roots as discriminant is greater than 0.