Question

** WILL FAN & MEDAL **
What is the approximate solution of this system of equations? :
y = x^2 + 3x + 3
y = x^2 + x + 2

A) (-0.5, 0.2)

B) (-0.5, 1.7)

C) (-0.1, 1.2)

D) (0.2, 1.5)

*I also ask if there is an easier way to solve this type of problem, is there a formula I can use with the calculator?*

Answer 1

If you have a graphing calculator, graph both equations on the same graph, and look for the points where the two cross. Those are the solutions.

Answer 2

just equate them

\[x^2 + 3x + 3 = x^2 +x+2\]

then solve for x

Answer 3

Subtract one equation from another
And try to solve the final equation you got after substraction.

Answer 4

@campbell_st has the easiest solution of all for this problem; I'm suggesting ways that you can do this for an arbitrary set of curves that may not be so easily solved this way.

Answer 5

when you find x, just substitute it into either equation to find y

Answer 6

Thanks a lot that helps!

Answer 7

In a multiple-choice situation like this, you could also evaluate the answer choices and see which one works.

For example, if you plug \(x=-0.5 = -1/2\) into the first equation\[x^2+3x+3 = (-1/2)^2+3(-1/2)+3 = 7/4 = 1.6\] and that is not close to the value given in the answer A, so A cannot be the right answer.

Answer 8

Oh okay I see

Answer 9

Remember that this problem asks which might be an APPROXIMATE solution, so you can't throw out an answer just because it isn't exactly correct...