algebra 2 help?

Question

Solve the system of equations using any method.
-5x - 4y + 12z = -140
9x - 8y + z = -649
3x - 2y + 6z = -290

Answer 1

Hi,

While the other methods work and get the same answer, to me "any method" means grab your calculator and use it. Enter the 3 equations into a 3 x 4 matrix as:

[-5.....-4....12..-140]
[.9.....-8.....1....-649]
[.3.....-2.....6....-290]

Go to MATRIX, CALC, and choose rref(

Enter the name of your matrix, so your screen shows rref([A]) and hit ENTER. The answer appears as:

[1..0..0..-40]
[0..1..0...34]
[0..0..1..-17]

This means x = -40, y = 34, and z = -17.

I think that's quicker and easier. I hope that helps!! :-)

Answer 2

solve by determinants:
x= -40, y=34, z= -17
equations:
-5x-4y+12z= -140
9x-8y+ z= -649
3x-2y+6z= -290
| -140 -4 12 |
| -649 -8 1 |
| -290 -2 6 |
x=_____________ = -20240/506 = -40

| -5 -4 12 |
| 9 -8 1 |
| 3 -2 6 |

solve for y:

| -5 -140 12 |
| 9 -649 1 |
| 3 -290 6 |
y=_______________ = 17204/506= 34
506

z= -649 +8y - 9x EQ. 2
subst x and y:
z= -649 + 8*34 -9*(-40) = -17

Answer 3

Equation 1: -5x - 4y + 12z = -140
Equation 2: 9x - 8y + z = -649
Equation 3: 3x - 2y + 6z = -290

Equation 2: z = -9x + 8y - 649
Substitute for z in Equations 1 and 3
Equation 1: -5x + 4y + 12(-9x+8y-649) = -140
Equation 3: 3x -2y +6(-9x+8y-649) = -290
Simplify
Equation 1: -5x +4y -108x +96y -7788 = -140
Equation 1: -113x + 100y = 7648
Equation 3: 3x - 2y -54x +48y -3894 = -290
Equation 3: -51x + 46y = 3604
Solve for y in Equation 1: y = 76.48 + 1.13x
Substitute for y in Equation 3:
-51x + 46(76.48 + 1.13x) = 3604
-51x + 3518.08 + 51.98x = 3604
.98x = 85.92
x = 87.673 (rounded)
y = 76.48 + 1.13x
y = 76.48 + 1.13(87.673) = 175.551 (rounded)
z = -9x + 8y - 649
z = -9(87.673) +8(175.551) - 649
z = 755.408 (rounded)

Answer 4

x=-40
y=34
z=-17
Use substition method.
1) leave top equation alone and multiply middle by -12. add those two equations together. Should get -113x+92y=7648. Save this answer
2) Multiply original middle equation by -6. Add this to the bottom equations. Should get -51x+46y=3604. Save this answer.
- These steps eliminate z.
3.) With the two new equations multiply equation is step 2 by
-2. You should get 102x-32y=-7208. Add this to the equation from Step 1. You should get -11x=440. Solve for X and you get -40
4.) Use either equation from step one or two and substitute
-40 for x. Using equation one you will get 92y=3128. y will equal 34.
5.)Using the values of x and y subsitute those numbers into any of the three and you will get z=-17.

Answer 5

These are always slow to solve. The solution is

x=-40
y=34
z=-17

Let's try adding equations together. Add -4 time Eq # 3 to Eq 2.

-3*x-23z=511 (Eq #4)

Add -2 time Eq #1 to Eq #2.

19*x -23*z = -369 (Eq #5)

Add Eq #4 to minus Eq #5.

22*x =-880 => x = -40

Now we can back substitute.

z = -17

y = 34