Question

6) Cramer’s Rule

Solve each using Cramer’s rule

a) 3x + .5y =10

10x - -y = -3

b) x + z +y = 12

-x + 3y - z = 2

-2x + z = -2

7) Proofs

Prove the following by induction

1. n^{3} – n is divisible by 3 for n
>=2

2. . Prove that *n*! <
*n ^{n}*

Prove directly that:

The sum of an integer and its cube is even.

Answer #1

**ANSWER 7 (2)**

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Use Cramer’s Rule to solve the system. x − 6y = 3 3x + 2y =
1

Solve the system of equations given below. 2x+5y+z= -1, 3x-5y-z=
6, 5x+y+3z= 10.

for 10-12 you will solve the following system of equations:
2x+y+z=-2 2x-y+3z=6 3x-5y+4z=7 10) what is the solution for x? a)2
b)-3 c)infinitely many solutions d)no solution 11) what is the
solution for y? a)2 b)0 c)inifinitely many solution d)no solution
12) what is the solution for z? a)4 b)-8 c)infinitely many
solutions d)no solutions

Solve the system using either Gaussian elimination with
back-substitution or Gauss-Jordan elimination.If the system has an
infinite number of solutions, express x, y, and
z in terms of the parameter t.)
3x + 3y + 9z = 6
x + y + 3z = 2
2x + 5y + 15z = 10
-x + 2y + 6z = 4
(x, y, z)
= ?

Solve each system by elimination.
1) -x-5y-5z=2
4x-5y+4z=19
x+5y-z=-20
2) -4x-5y-z=18
-2x-5y-2z=12
-2x+5y+2z=4
3) -x-5y+z=17
-5x-5y+5z=5
2x+5y-3z=-10
4) 4x+4y+z=24
2x-4y+z=0
5x-4y-5z=12
5) 4r-4s+4t=-4
4r+s-2t=5
-3r-3s-4t=-16
6) x-6y+4z=-12
x+y-4z=12
2x+2y+5z=-15

Section B.3 - Algebra - Simultaneous and Quadratic Equations
Solve problems 1 and 2 using the comparison, elimination, or
substitution method.
1) x +y =2 2x -3y =5
2 ) 3x - 5y=5 7x + y = 75

Solve the following system of equations.
{−x+4y−z=-4
3x−y+2z=6
2x−3y+3z=−2
Give your answer as an ordered triple
(x,y,z).

solve the following pairs of simultaneous equations
a) x=7y+3
y=3x-7
b) 2x+5y =23
5x-2y=14

1-solve for x and y
3x+(y-2)i=(5-2x)+(3y-8)i
2-solve for z and write the answer with standard form
(3-2i)z+(4i+6)=8i
3-preform the indicated operation and write the answer with
standard form
(9+5i)-(6+2i)

Use
Gaussian Elimination to solve and show all steps:
1. (x+4y=6)
(1/2x+1/3y=1/2)
2. (x-2y+3z=7)
(-3x+y+2z=-5)
(2x+2y+z=3)

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