Answer:
No solutions
Step-by-step explanation:
Let's solve your equation step-by-step.
3(6d−24)=6(12+3d)
Step 1: Simplify both sides of the equation.
3(6d−24)=6(12+3d)
(3)(6d)+(3)(−24)=(6)(12)+(6)(3d)(Distribute)
18d+−72=72+18d
18d−72=18d+72
Step 2: Subtract 18d from both sides.
18d−72−18d=18d+72−18d
−72=72
Step 3: Add 72 to both sides.
−72+72=72+72
0=144
Answer:
There are no solutions.
<em>Note: I am assuming your second equation is:</em>
<em>x = 2y - 1</em>
<em></em>
Answer:
The solution to the system of equations is:
Step-by-step explanation:
Given the system of equations
2x+y=3
x = 2y - 1
solving the system of equations using the elimination method
![\begin{bmatrix}2x+y=3\\ x=2y-1\end{bmatrix}](https://tex.z-dn.net/?f=%5Cbegin%7Bbmatrix%7D2x%2By%3D3%5C%5C%20x%3D2y-1%5Cend%7Bbmatrix%7D)
Arrange equation variables for elimination
![\begin{bmatrix}2x+y=3\\ x-2y=-1\end{bmatrix}](https://tex.z-dn.net/?f=%5Cbegin%7Bbmatrix%7D2x%2By%3D3%5C%5C%20x-2y%3D-1%5Cend%7Bbmatrix%7D)
Multiply x-2y=-1 by2: 2x-4y=-2
![\begin{bmatrix}2x+y=3\\ 2x-4y=-2\end{bmatrix}](https://tex.z-dn.net/?f=%5Cbegin%7Bbmatrix%7D2x%2By%3D3%5C%5C%202x-4y%3D-2%5Cend%7Bbmatrix%7D)
subtracting the equations
![2x-4y=-2](https://tex.z-dn.net/?f=2x-4y%3D-2)
![-](https://tex.z-dn.net/?f=-)
![\underline{2x+y=3}](https://tex.z-dn.net/?f=%5Cunderline%7B2x%2By%3D3%7D)
![-5y=-5](https://tex.z-dn.net/?f=-5y%3D-5)
now solve -5y = -5 for y
![-5y=-5](https://tex.z-dn.net/?f=-5y%3D-5)
Divide both sides by -5
![\frac{-5y}{-5}=\frac{-5}{-5}](https://tex.z-dn.net/?f=%5Cfrac%7B-5y%7D%7B-5%7D%3D%5Cfrac%7B-5%7D%7B-5%7D)
Simplify
![y=1](https://tex.z-dn.net/?f=y%3D1)
For 2x+y=3 plug in y=1
![2x+1=3](https://tex.z-dn.net/?f=2x%2B1%3D3)
subtract 1 from both sides
![2x+1-1=3-1](https://tex.z-dn.net/?f=2x%2B1-1%3D3-1)
Simplify
![2x=2](https://tex.z-dn.net/?f=2x%3D2)
Divide both sides by 2
![\frac{2x}{2}=\frac{2}{2}](https://tex.z-dn.net/?f=%5Cfrac%7B2x%7D%7B2%7D%3D%5Cfrac%7B2%7D%7B2%7D)
Simplify
![x=1](https://tex.z-dn.net/?f=x%3D1)
Therefore, the solution to the system of equations is:
Hints:
1) This is an arithmetic sequence.
2) The first member of the sequence is 4.
3) The common difference is 6. To each member, we add 6 to get the next.
4) The formula for the nth term of an arith. sequence is as follows:
l=a + (n-1)d, where l is the LAST term, n is the number of terms, d is the common difference, and a is the first term. Write this out. Play with n, increasing (integer) n until this formula predicts numbers close to 576. Do you get exactly 576 for one of these INTEGER n values? If yes, then 576 is a member of the sequence. If no, then it is not.
Answer:
-4x + y + 6z
Step-by-step explanation:
2x + 5y - z + (-6x - 4y + 7z) < distribute positive 1 to (-6x - 4y + 7z)
2x + 5y - z - 6x - 4y + 7z < combine like terms to get the answer
2x - 6x = -4x
5y - 4y = y
-z + 7z = 6z
our new expression is:
-4x + y + 6z we cannot simplify this any further, so this is our answer