Question

Solve the system of equations: y= 3x y= x^2 - 4

Answer 1

`x=-1\\y=-3\\\\x=4\\y=12`

Explanation:

Make both equations equal to each other and solve for the variable x:

`y=y\\3x=x^2-4\\x^2-3x-4=0\\`

Find two numbers that when you add them you get -3 and the product of both numbers be -4. These numbers are 1 and -4. Then:

`(x+1)(x-4)=0\\\\x+1=0\\x=-1\\\\x-4=0\\x=4`

Substitute these values into one the original equations and solve for y:

`y=3(-1)\\y=-3\\\\y=3(4)\\y=12`

Therefore, you get that:

`x=-1\\y=-3\\\\x=4\\y=12`