Question

Solve the system of equations. y= 4x + 5 y=x2+12x+20

Answer 1

x1 = -3

x2 = -5

y1 = -7

y2 = -15

Explanation:

y = 4x +5

y = x2+12x+20

substitute y in second equation with first and solve quadratic equation

4x+5 = x² +12x + 20

x²+8x + 15 =0

D= b² - 4ac

a = 1

b = 8

c = 15

D = 64 - 60 = 4

D>0 => 2 real roots

x1 =
`(-b+√(D) )/(2a)`= (-8+2)/2 = -3

x2 =
`(-b-√(D) )/(2a)` = (-8-2)/2 = -5

having roots of x we can calculate y

y1 = 4x1+5 = 4*-3 +5 = -12 +5 = -7

y2 =4x2+5 = 4*-5+5 = -20 + 5 = -15

x1 = -3

x2 = -5

y1 = -7

y2 = -15