Question

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

Answer 1

`y=-10x^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
`10x^2+y+2=0`

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

To evaluate it for `x=3`, just plug it into the function to get
`y(3)=-10(3)^2-2=-10(9)-2=-90-2=-92`

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

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

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