Solve for n. n−10=5−4n
2 answers:
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Answer:
1) {y,x}={-3,-23}
2) {x,y}={7,-9/2}
Step-by-step explanation:
Required:
- Solve systems of equations
1) y - x = 20, 2x - 15y = -1
Equations Simplified or Rearranged :
[1] y - x = 20
[2] -15y + 2x = -1
Graphic Representation of the Equations :
x + y = 20 2x - 15y = -1
Solve by Substitution :
// Solve equation [1] for the variable y
[1] y = x + 20
// Plug this in for variable y in equation [2]
[2] -15•(x +20) + 2x = -1
[2] - 13x = 299
// Solve equation [2] for the variable x
[2] 13x = - 299
[2] x = - 23
// By now we know this much :
y = x+20
x = -23
// Use the x value to solve for y
y = (-23)+20 = -3
Solution :
{y,x} = {-3,-23}
2) 25-x=-4y,3x-2y=30
Equations Simplified or Rearranged :
[1] -x + 4y = -25
[2] 3x - 2y = 30
Graphic Representation of the Equations :
4y - x = -25 -2y + 3x = 30
Solve by Substitution :
// Solve equation [1] for the variable x
[1] x = 4y + 25
// Plug this in for variable x in equation [2]
[2] 3•(4y+25) - 2y = 30
[2] 10y = -45
// Solve equation [2] for the variable y
[2] 10y = - 45
[2] y = - 9/2
// By now we know this much :
x = 4y+25
y = -9/2
// Use the y value to solve for x
x = 4(-9/2)+25 = 7
Solution :
{x,y} = {7,-9/2}
You know 1 is not a root because the sum of the coeffcients of the equation is 14, not zero.
It is fairly easy to try 3 by synthetic division (see attachment), which tells you that 3 is a root and the remaining quadratic factor is x²-3x-5. The quadratic formula tells you the roots of that factor are
... x = (-b±√(b²-4ac))/(2a) = (3±√29)/2
The appropriate choices are
... C. (3-√29)/2
... D. (3+√29)/2
... F. 3
_____
The quadratic formula tells you the solution to
... ax²+bx+c=0
is x = (-b±√(b²-4ac))/(2a)
We have a=1, b=-3, c=-5.
EDIT: Picture
33) When adding matrices, just add the numbers that are in the same spot. In this problem we are given A and C, and we are asked to find B if A + B = C
So B = C - A
![\left[\begin{array}{ccc}2&-1&-3\\1&4&-2\\\end{array}\right]](https://tex.z-dn.net/?f=%20%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D2%26-1%26-3%5C%5C1%264%26-2%5C%5C%5Cend%7Barray%7D%5Cright%5D)
- ![\left[\begin{array}{ccc}4&9&-2\\-3&5&7\\\end{array}\right]](https://tex.z-dn.net/?f=%20%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D4%269%26-2%5C%5C-3%265%267%5C%5C%5Cend%7Barray%7D%5Cright%5D%20)
= ![\left[\begin{array}{ccc}-2&-10&-1\\4&-1&-9\\\end{array}\right]](https://tex.z-dn.net/?f=%20%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D-2%26-10%26-1%5C%5C4%26-1%26-9%5C%5C%5Cend%7Barray%7D%5Cright%5D%20)
34) When multiplying matrices, the number of columns in the first matrix needs to be the same as the number of rows in the second matrix. Then the outcome will have the same number of rows as the first matrix and same number of columns as the second matrix. In this case, the result will be a 2x2.
33) When adding matrices, just add the numbers that are in the same spot. In this problem we are given A and C, and we are asked to find B if A + B = C
So B = C - A
34) When multiplying matrices, the number of columns in the first matrix needs to be the same as the number of rows in the second matrix. Then the outcome will have the same number of rows as the first matrix and same number of columns as the second matrix. In this case, the result will be a 2x2.