kaliitcri

2022-02-05

How do you simplify the expression $7{x}^{2}-4y+3{x}^{2}+5y+2$ and evaluate it for ?

Jonathan Mckenzie

Expert

$y=-10{x}^{2}-2$
$?x=3-y=-92$
$?y=x+3$- No real solution
$y=9$- 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
$\frac{-{\left(1\right)}^{2}±\sqrt{{\left(1\right)}^{2}-4\left(10\right)\left(5\right)}}{2\left(10\right)}$
$\frac{-1±\sqrt{1-200}}{20}$
$\frac{-1±\sqrt{-199}}{20}$
This results in undefined so there are no real solutions.
For $y=9$ we do the following
$9=-10{x}^{2}-2$
$-10{x}^{2}=11$
${x}^{2}=\frac{11}{-10}$
$x=\sqrt{-\frac{11}{10}}$
This is also undefined, so there are no real solutions.

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