Question

solve the linear / quadratic system and give the values of x that satisfy it5x²+2x+5=yy-6=2x

Answer 1

From the second equation we solve for y to get:

$y=2x+6$

Plugging the above value of y into the first equation gives

$5x^2+2x+5=2x+6$

Subtracting 2x from both sides gives

$5x^2+5=6$

and subtracting 5 from both sides gets us

$5x^2=1$

Finally, divide both sides by 5 and then take the square root to get

$\textcolor{#FF7968}{x=\pm\frac{1}{\sqrt[]{5}}}$

which is our answer!