Answer: F
Step-by-step explanation:
- This does not have infinitely many solutions (adding the equations, we get a fixed value of x)
- This has no solutions (the left hand sides are the same but the right hand sides have different values)
- This has one solution (the first equation givess a fixed value for x)
- This has no solutions (same reason as 2)
- This has one solution (same reason as 3, just the second equation instead of the first)
- This has infinitely many solutions (multiplying both sides of the top equation by -2 gives the bottom equation).
now, bear in mind that all these ones are lines, and to graph a line all you need is two points, so let's pick a couple of random values for say "x" and let's see what we get for "y" and that's our x,y point.
3)
![9x+4y=-16\implies \stackrel{\textit{using x = 0}~\hfill }{9(0)+4y=-16}\implies 4y=-16 \\\\\\ y=\cfrac{-16}{4}\implies y=-4~\hspace{10em}(0~~,~~-4) \\\\[-0.35em] ~\dotfill\\\\ 9x+4y=-16\implies \stackrel{\textit{using x = -4}~\hfill }{9(-4)+4y=-16}\implies -36+4y=-16 \\\\\\ 4y=20\implies y = \cfrac{20}{4}\implies y = 5~\hspace{10em}(-4~~,~~5)](https://tex.z-dn.net/?f=9x%2B4y%3D-16%5Cimplies%20%5Cstackrel%7B%5Ctextit%7Busing%20x%20%3D%200%7D~%5Chfill%20%7D%7B9%280%29%2B4y%3D-16%7D%5Cimplies%204y%3D-16%20%5C%5C%5C%5C%5C%5C%20y%3D%5Ccfrac%7B-16%7D%7B4%7D%5Cimplies%20y%3D-4~%5Chspace%7B10em%7D%280~~%2C~~-4%29%20%5C%5C%5C%5C%5B-0.35em%5D%20~%5Cdotfill%5C%5C%5C%5C%209x%2B4y%3D-16%5Cimplies%20%5Cstackrel%7B%5Ctextit%7Busing%20x%20%3D%20-4%7D~%5Chfill%20%7D%7B9%28-4%29%2B4y%3D-16%7D%5Cimplies%20-36%2B4y%3D-16%20%5C%5C%5C%5C%5C%5C%204y%3D20%5Cimplies%20y%20%3D%20%5Ccfrac%7B20%7D%7B4%7D%5Cimplies%20y%20%3D%205~%5Chspace%7B10em%7D%28-4~~%2C~~5%29)
check the red line in the picture below.
4)
check the blue line in the picture below.
Step-by-step explanation:
(3x + 2y =19)(3)
-9x + 8y =-29
9x + 6y = 57 <em><u>NOTE</u></em><em><u>:</u></em> we cross here 9x in first
-9x + 8y = -29 we cross here - 9x in second
Since 9x and - 9x are opposite
___________
6y +8y = 57 - 29
14y = 28
Y=28/14
Y=2
Replace y in second equation of this system:
-9x + 8y = - 29
-9x +8(2)= - 29
-9x + 16 = - 29
-9x = -29 - 16
-9x = - 45
X= -45/-9
X=5
Hope this helps..
Answer:
x= 25
Step-by-step explanation:
Answer:
b
Step-by-step explanation:
