Question

Solve the following system of equations and show all work.

y = 2x2
y = –3x −1

Answer 1

What's the first equation?

Answer 2

y=2x^2

Answer 3

set \[2x^2=-3x+1\] and solve for \(x\)

Answer 4

5x^2

Answer 5

You're supposed to solve for x as a numerical answer. Are you familiar with quadratic formula?

Answer 6

since y - y = 0, 2x^2 - (-3x-1) = 0, 2x^2 + 3x + 1 = 0, x^2 + (3/2)x + 1/2 = 0, guess common factors between 1 and 1/2 that add up to 3/2? guess that's just 1 and 1/2 no need to use the formula, so (x+1)(x+1/2) = 0 x = -1/2 or x = -1

if you want to use the formula, it's (-b + or - sqrt( b^2 - 4ac) )/2a where ax^2 + bx + c = 0 in this case a = 2, b = 3, and c = 1.

Answer 7

Yes. To clean up with Kenshin said:
`QUADRATIC FORMULA:`
\[\huge \frac{ -b \pm \sqrt{b^2-4ac} }{ 2a }\]
a = 2, b = 3, c =1. In this case, it might be quicker to use the formula than to think of factors with fractions. At least this way as long as you do the algebra correct (which is VERY easy in this case) then you'll be fine!

I think that students are too afraid to use this equation because they don't use it enough. It's considered "long" and they don't try to memorize it. Once you do, it can become your best friend.