Question

Solve the system of equations.
y = 2x+ 3
y=x^2+3x+3

Answer 1

(0,3)

(-1,1)

Explanation:

Hello!

Since both equations are equal to y, we can set the right-hand side of the equations equal to each other.

• 
  `y = 2x + 3\\y = x^2 + 3x + 3`
• 
  `y = y`
• 
  `2x + 3 = x^2 + 3x + 3`

Solve for x

• 
  `2x + 3 = x^2 + 3x + 3`
• 
  `0 = x^2 + x`
• 
  `0 = x(x + 1)`
• 
  `x = 0, x =-1`

X can either be 0 or -1. Remember, a solution to a system is not complete without a y-value. Plug in 0 and -1 for x in the first equation, and find the corresponding y-values.

`y = 2(0) + 3\\y = 3`

And

`y = 2(-1) + 3\\y = -2 + 3\\y = 1`

So the solutions to the system are (0,3) and (-1,1)