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!