Question

How many solutions does the system have?
Y=4x+4
Y=x^2+4

Answer 1

2 solutions (0, 4) and (4, 20)

Explanation:

you can solve by substitution

y=4x+4 and y=x²+4 so you can say that

4x+4=x²+4

subtract (4x+4) from both sides to get an equation that equals 0

0=x²-4x (the 4 cancels itself out, 4-4)

simplify, solve for x

0=x(x-4)

set each part =0 and solve

x=0 x-4=0

so x=0 and x=4

plug each solution back into one of the equations

y=4(0)+4

y=4

(0, 4) is one solution

y=4(4)+4

y=20

(4, 20) is another solution

so you have 2 solutions, (0, 4) and (4, 20)