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3 years ago

HELP! What is the solution to this system of equations?

Mathematics

2 answers:

goblinko [34]3 years ago

5 0

5x - 3y + z = -6
x + 3y - z = 0
-------------------add
6x = -6
x = -1 <===

x + 3y - z = 0
4x + y + z = 7
------------------add
5x + 4y = 7

5(-1) + 4y = 7
-5 + 4y = 7
4y = 7 + 5
4y = 12
y = 12/4
y = 3 <===

5x - 3y + z = -6
5(-1) - 3(3) + z = -6
-5 - 9 + z = -6
-14 + z = -6
z = -6 + 14
z = 8 <===

notsponge [240]3 years ago

5 0

First one

Simplifying
5x + -3y + z = -6

Solving
5x + -3y + z = -6

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.
Add '3y' to each side of the equation. 5x + -3y + 3y + z = -6 + 3y

Add '3y' to each side of the equation.
5x + -3y + 3y + z = -6 + 3y

Combine like terms: -3y + 3y = 0
5x + 0 + z = -6 + 3y
5x + z = -6 + 3y

Add '-1z' to each side of the equation.
5x + z + -1z = -6 + 3y + -1z

Combine like terms: z + -1z = 0
5x + 0 = -6 + 3y + -1z
5x = -6 + 3y + -1z

Divide each side by '5'.
x = -1.2 + 0.6y + -0.2z

Simplifying
x = -1.2 + 0.6y + -0.2z

Second one

Simplifying
x + 3y + -1z = 0

Solving
x + 3y + -1z = 0


Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.


Add '-3y' to each side of the equation.
x + 3y + -3y + -1z = 0 + -3y

Combine like terms: 3y + -3y = 0
x + 0 + -1z = 0 + -3y
x + -1z = 0 + -3y
Remove the zero:
x + -1z = -3y

Add 'z' to each side of the equation.
x + -1z + z = -3y + z

Combine like terms:
-1z + z = 0 x + 0 = -3y + z
x = -3y + z

Simplifying x = -3y + z

Third one

Simplifying
4x + y + z = 7 

Solving
4x + y + z = 7

Solving for variable 'x'.


Move all terms containing x to the left, all other terms to the right.

Add '-1y' to each side of the equation.
4x + y + -1y + z = 7 + -1y

Combine like terms: y + -1y = 0
4x + 0 + z = 7 + -1y
4x + z = 7 + -1y

Add '-1z' to each side of the equation.
4x + z + -1z = 7 + -1y + -1z

Combine like terms: z + -1z = 0
4x + 0 = 7 + -1y + -1z
4x = 7 + -1y + -1z

Divide each side by '4'.
x = 1.75 + -0.25y + -0.25z

Simplifying
x = 1.75 + -0.25y + -0.25z

Hope all of this helps

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