# How do you simplify the expression 7x^2-4y+3x^2+5y+2 and evaluate it for x+3 and y=9?

Apr 27, 2017

$y = - 10 {x}^{2} - 2$
? $x = 3$ - $y = - 92$
? $y = x + 3$ - No real solutions
$y = 9$ - No real solutions

#### Explanation:

Assuming this is all equal to 0, we add like terms
$10 {x}^{2} + y + 2 = 0$

We can then isolate one of the variables, usually $y$.
$y = - 10 {x}^{2} - 2$

To evaluate it for $x = 3$, just plug it into the function to get
$y \left(3\right) = - 10 {\left(3\right)}^{2} - 2 = - 10 \left(9\right) - 2 = - 90 - 2 = - 92$

To solve for $y = x + 3$ we get
$x + 3 = - 10 {x}^{2} - 2$
$10 {x}^{2} + x + 5 = 0$

We can use the quadratic formula to get the solutions
$\setminus \frac{- {\left(1\right)}^{2} \setminus \pm \setminus \sqrt{{\left(1\right)}^{2} - 4 \left(10\right) \left(5\right)}}{2 \left(10\right)}$
$\setminus \frac{- 1 \setminus \pm \setminus \sqrt{1 - 200}}{20}$
$\setminus \frac{- 1 \setminus \pm \setminus \sqrt{- 199}}{20}$
This results in undefined so there are no real solutions.

For $y = 9$ we do the following
$9 = - 10 {x}^{2} - 2$
$- 10 {x}^{2} = 11$
${x}^{2} = \frac{11}{-} 10$
$x = \setminus \sqrt{- \frac{11}{10}}$
This is also undefined, so there are no real solutions.