SOLUTION: Please help me solve this equation: 5x-6x=-17 3x-4y+5z=-1 2z=-6. This is one problem or equation. Thank you I appreciate if you can help me understand the process involved with sol

Algebra ->  Expressions-with-variables -> SOLUTION: Please help me solve this equation: 5x-6x=-17 3x-4y+5z=-1 2z=-6. This is one problem or equation. Thank you I appreciate if you can help me understand the process involved with sol      Log On


   

Question 239735: Please help me solve this equation: 5x-6x=-17 3x-4y+5z=-1 2z=-6. This is one problem or equation. Thank you I appreciate if you can help me understand the process involved with solving this type of equation.
Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
5x - 6x = -17
3x - 4y + 5z = -1
2z = -6

looks like you have 3 equations that have to be solved simultaneously.

looks like your third equation has already solved for z so we can start there.

2z = -6 becomes z = -3 when you divided both sides of the equation by 2.

z = -3 is the value of one of your variables.

you are left with:

5x - 6x = -17
3x - 4y + 5z = -1

that first equation looks like it's all in x so we can solve for x from that equation.

5x - 6x = -17 becomes -x = -17 after you combine like terms.

multiply both sides of this equation by -1 to get:

x = 17

you now have two values out of the 3.

you have:

x = 17
z = -3

you have only one equation left to solve.

that is:

3x - 4y + 5z = -1

replace x with 17 and z with -3 in that equation to get:

3*(17) - 4*y + 5*(-3) = -1

this becomes:

51 - 4*y - 15 = -1

combine like terms to get:

36 - 4*y = -1

add 4*y to both sides of the equation and add 1 to both sides of the equation to get:

36 + 1 = 4*y

combine like terms to get:

37 = 4*y

divide both sides of the equation by 4 to get:

9.25 = y

this is the same as:

y = 9.25

the answer to your equation is:

x = 17
y = 9.25
z = -3

substitute in your original equations to confirm these answers are good.

5x - 6x = -17
3x - 4y + 5z = -1
2z = -6

these become:

5*(17) - 6*(17) = -17
3*(17) - 4*(9.25) + 5*(-3) = -1
2*(-3) = -6

simplify and combine like terms to get:

-17 = -17
51 - 37 - 15 = -1
-6 = -6

simplify further to get:

-17 = -17
-1 = -1
-6 = -6

all equations confirm so the answer is good.