Is it multiple choice? If so, leave the answer choices.
So first one
'how many solutions does 2x-y=-5 and 2x+y=5 have?'
add and get
2x-y-5
plus
2x+y=5
equals
2x+2x+y-y=5-5
4x=0
x=0 always
solve for y
4(0)+y=5
y=5
the solution is (0,5)
only <u>ONE </u>solution
one way is to subsitute
just remember that it is in (x,y) form so
the pont (1,2) means that 1 solution is x=1 and y=2 so subsitute and find that
the first one is the answer you are correct
just look at the graph
the solution is the intersection
it seems to be at a point that is 3 units to the right and -6 units up (6 units down)
so the solution is (3,-6)
yo are corect
subsitution
y=y
therefor
the answe ris (-4,-14) if you did the math correctly
#8 is correct
# 9 is correct
# 10 the answe ris bananas=0.40 pears=0.60
the last one you got it wrong, remember to check your answer to the graph for commonsense
then answer is (-2,5) and (1,2)
For the complex roots I got 1,2,-3
![tan \frac{x}{2} =\pm \sqrt{\frac{1-cos x}{1+cos x}}](https://tex.z-dn.net/?f=tan%20%5Cfrac%7Bx%7D%7B2%7D%20%3D%5Cpm%20%5Csqrt%7B%5Cfrac%7B1-cos%20x%7D%7B1%2Bcos%20x%7D%7D)
Find cos using trig identities:
![sec x = \frac{1}{cos x} \\ tan^2 x = sec^2 x -1](https://tex.z-dn.net/?f=sec%20x%20%3D%20%5Cfrac%7B1%7D%7Bcos%20x%7D%20%20%5C%5C%20tan%5E2%20x%20%3D%20sec%5E2%20x%20-1)
Therefore
![cos x = \frac{1}{sec x} =\pm \frac{1}{\sqrt{tan^2 x +1}}](https://tex.z-dn.net/?f=cos%20x%20%3D%20%5Cfrac%7B1%7D%7Bsec%20x%7D%20%3D%5Cpm%20%5Cfrac%7B1%7D%7B%5Csqrt%7Btan%5E2%20x%20%2B1%7D%7D)
Sub in tan x = 3, (Note that x is in 3rd quadrant, cos x < 0)
![cos x =- \frac{1}{\sqrt{3^2 +1}} = -\frac{1}{\sqrt{10}}](https://tex.z-dn.net/?f=cos%20x%20%3D-%20%5Cfrac%7B1%7D%7B%5Csqrt%7B3%5E2%20%2B1%7D%7D%20%3D%20-%5Cfrac%7B1%7D%7B%5Csqrt%7B10%7D%7D)
Finally, sub into Half-angle formula:(Note x/2 is in 2nd quadrant, tan x<0)