(2,-6,1)
There are a few way to solve this with linear programming, but I am using a simple substitution method.
The goal is to isolate the variables by subtracting or adding the equations. (note: I will refer to the equations as A,B, and C)
2x+y−z=−3
5x−2y+2z=24
3x−z=5
C already has just two variables, x and z. This means a good place to start is by eliminating at least y from one other equation, if not y and another value. To do this, we need to either add two equations where the y values are opposite or subtract one where the y value is equal. However, the two equations with a y value do not have opposite or the same y values.
To get a new equation, we can multiply A by 2. This will give us +2y, which can be added to B to eliminate the value all together- AND the z value. Remember that the WHOLE A equation needs to be multiplied by 2:
2(2x+y-z)=2(-3)
4x+2y-2z=-6
We can now add 2A to B.
(4x+2y-2z=-6)+(5x−2y+2z=24
)
9x=18
x=2
We now know x=2. We can plug this into C to find the z value.
3x−z=5
3(2)-z=5
6-z=5
-z=-1
z=1
With both x and z, we can find y using A.
2x+y−z=−3
2(2)+y-(1)=-3
4+y-1=-3
3+y=-3
y=-6
x=2, y=-6, z=1
Answer:
See below.
Step-by-Step Explanation:
5)<em> 8x+9-6x-7</em>
8x + 2 - 6x (Subtract the numbers)
2x + 2 (Combine like terms)
2 (x + 1) (Common factor - Factor by grouping twice)
6) <em>2y-6+5y+9</em>
2y + 3 + 5y (Add the numbers)
7y + 3 (Combine like terms)
7) <em>3x+8+4x-9</em>
3x - 1 + 4x (Subtract the numbers)
7x - 1 (Combine like terms)
8) <em>9y+16-12y+24</em>
9y + 40 - 12y (Add the numbers)
-3y + 40 (Combine like terms)
9) <em>7g-5-8g+12</em>
7g + 7 - 8g (Add the numbers)
-g + 7 (Combine like terms)
10)<em> 11c-8+5c-8</em>
11c - 16 + 5c (Subtract the numbers)
16c - 16 (Combine like terms)
16 (c - 1) (Common factor - Factor by grouping twice)
11) <em>5(2x + 3) (This one was a bit blurry, I am assuming that's a addition sign.)</em>
10x + 15 (Distribute)
12) <em>5(-2x+3)</em>
-10x + 15 (Distribute)
Hope this helps!
The solution to the quadratic equation is option D
Answer: 240
Step-by-step explanation:
Distribute all numbers
24 - 6(-21)
24 - (-126)
24+216
240
Answer:
11 will be shared out and there will be 2 rubbers left.
Step-by-step explanation:
the last number that 3 goes into before 35 is 33. 33 ÷ 3 = 11. So each friend gets 11 rubbers. then from 33, there will be 2 rubbers left.
