Answer:
y = 50x
Step-by-step explanation:
the equation for this is y = 50x because for every 50 units we go up by on the graph we go 1 unit to the right so:
slope-intercept form: y = mx + b where m is the slope and b is the y-intercept. Our y-intercept is 0 because that is where our line intersects the y-axis and because it is 0 we do not need to put it in the equation.
y = 50x
Answer:
(- 3, 5 )
Step-by-step explanation:
Given the 2 equations
y = - x + 2 → (1)
y = - 2x - 1 → (2)
Using substitution method.
Substitute y = - x + 2 into (2)
- x + 2 = - 2x - 1 ( add 2x to both sides )
x + 2 = - 1 ( subtract 2 from both sides )
x = - 3
Substitute x = - 3 into (1)
y = - (- 3) + 2 = 3 + 2 = 5
Solution is (- 3, 5 )
It would be B because you would take amelias age and take two away since todd is five years younger to get the a-5.
hope this helps :)
Add 5 to both sides
5-5+x/3=5-11
0+x/3=-6
x/3=-6
times both sides by 3
3x/3=-18
x=-18
The given system of equations in augmented matrix form is
![\left[\begin{array}{cccc|c}3&2&-4&2&-23\\-6&1&2&4&-12\\1&-3&-3&5&-20\\-2&5&6&0&12\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bcccc%7Cc%7D3%262%26-4%262%26-23%5C%5C-6%261%262%264%26-12%5C%5C1%26-3%26-3%265%26-20%5C%5C-2%265%266%260%2612%5Cend%7Barray%7D%5Cright%5D)
If you need to solve this, first get the matrix in RREF:
- Add 2(row 1) to row 2, row 1 to -3(row 3), and 2(row 1) to 3(row 4):
![\left[\begin{array}{cccc|c}3&2&-4&2&-23\\0&5&-6&8&-58\\0&11&5&-13&37\\0&19&10&4&-10\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bcccc%7Cc%7D3%262%26-4%262%26-23%5C%5C0%265%26-6%268%26-58%5C%5C0%2611%265%26-13%2637%5C%5C0%2619%2610%264%26-10%5Cend%7Barray%7D%5Cright%5D)
- Add 11(row 2) to -5(row 3), and 19(row 1) to -5(row 4):
![\left[\begin{array}{cccc|c}3&2&-4&2&-23\\0&5&-6&8&-58\\0&0&-91&153&-823\\0&0&-164&132&-1052\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bcccc%7Cc%7D3%262%26-4%262%26-23%5C%5C0%265%26-6%268%26-58%5C%5C0%260%26-91%26153%26-823%5C%5C0%260%26-164%26132%26-1052%5Cend%7Barray%7D%5Cright%5D)
- Add 164(row 3) to -91(row 4):
![\left[\begin{array}{cccc|c}3&2&-4&2&-23\\0&5&-6&8&-58\\0&0&-91&153&-823\\0&0&0&13080&-39240\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bcccc%7Cc%7D3%262%26-4%262%26-23%5C%5C0%265%26-6%268%26-58%5C%5C0%260%26-91%26153%26-823%5C%5C0%260%260%2613080%26-39240%5Cend%7Barray%7D%5Cright%5D)
- Multiply row 4 by 1/13080:
![\left[\begin{array}{cccc|c}3&2&-4&2&-23\\0&5&-6&8&-58\\0&0&-91&153&-823\\0&0&0&1&-3\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bcccc%7Cc%7D3%262%26-4%262%26-23%5C%5C0%265%26-6%268%26-58%5C%5C0%260%26-91%26153%26-823%5C%5C0%260%260%261%26-3%5Cend%7Barray%7D%5Cright%5D)
- Add -153(row 4) to row 3:
![\left[\begin{array}{cccc|c}3&2&-4&2&-23\\0&5&-6&8&-58\\0&0&-91&0&-364\\0&0&0&1&-3\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bcccc%7Cc%7D3%262%26-4%262%26-23%5C%5C0%265%26-6%268%26-58%5C%5C0%260%26-91%260%26-364%5C%5C0%260%260%261%26-3%5Cend%7Barray%7D%5Cright%5D)
![\left[\begin{array}{cccc|c}3&2&-4&2&-23\\0&5&-6&8&-58\\0&0&1&0&4\\0&0&0&1&-3\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bcccc%7Cc%7D3%262%26-4%262%26-23%5C%5C0%265%26-6%268%26-58%5C%5C0%260%261%260%264%5C%5C0%260%260%261%26-3%5Cend%7Barray%7D%5Cright%5D)
- Add 6(row 3) and -8(row 4) to row 2:
![\left[\begin{array}{cccc|c}3&2&-4&2&-23\\0&5&0&0&-10\\0&0&1&0&4\\0&0&0&1&-3\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bcccc%7Cc%7D3%262%26-4%262%26-23%5C%5C0%265%260%260%26-10%5C%5C0%260%261%260%264%5C%5C0%260%260%261%26-3%5Cend%7Barray%7D%5Cright%5D)
![\left[\begin{array}{cccc|c}3&2&-4&2&-23\\0&1&0&0&-2\\0&0&1&0&4\\0&0&0&1&-3\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bcccc%7Cc%7D3%262%26-4%262%26-23%5C%5C0%261%260%260%26-2%5C%5C0%260%261%260%264%5C%5C0%260%260%261%26-3%5Cend%7Barray%7D%5Cright%5D)
- Add -2(row 2), 4(row 3), and -2(row 4) to row 1:
![\left[\begin{array}{cccc|c}3&0&0&0&3\\0&1&0&0&-2\\0&0&1&0&4\\0&0&0&1&-3\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bcccc%7Cc%7D3%260%260%260%263%5C%5C0%261%260%260%26-2%5C%5C0%260%261%260%264%5C%5C0%260%260%261%26-3%5Cend%7Barray%7D%5Cright%5D)
![\left[\begin{array}{cccc|c}1&0&0&0&1\\0&1&0&0&-2\\0&0&1&0&4\\0&0&0&1&-3\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bcccc%7Cc%7D1%260%260%260%261%5C%5C0%261%260%260%26-2%5C%5C0%260%261%260%264%5C%5C0%260%260%261%26-3%5Cend%7Barray%7D%5Cright%5D)
So the solution to this system is 
.
