Question

8x + 6y - z= 10-7X - 3y + z = 54x + 3y + z = 8z=y =x =​

Answer 1

To solve the given system of equations, we simplify and combine the equations to find one variable and then back-substitute to find the others, finally verifying our solution with the original equations. The solution is x = 9, y = -28/3, and z = 6.

Step-by-step explanation:

To solve the system of equations for all three variables, we follow a step-by-step algebraic process:

1. Eliminate terms wherever possible to simplify the equations.
2. Combine equations to find one of the variables, then back-substitute to find the others.
3. Check the solution to see if it satisfies all the original equations.

Lets start by adding the second and third equations:

(-7x - 3y + z) + (4x + 3y + z) = 5 + 8

-3x + 2z = 13

Now, we can solve for z by using the first equation:

8x + 6y - z = 10

Let's denote -3x + 2z = 13 as Equation (4). We can express z from the first equation as:

z = 8x + 6y - 10

Substitute z into Equation (4):

-3x + 2(8x + 6y - 10) = 13

13x +12y = 33

Now we have a new system of equations:

13x + 12y = 33

4x + 3y = 8

We can multiply the second equation by 3 and subtract from the first to eliminate y:

13x + 12y - (12x + 9y) = 33 - 24

x = 9

Now substitute x into the second original equation to find y:

4(9) + 3y = 8

3y = 8 - 36

3y = -28

y = -28 / 3

Finally, substitute x and y into the first original equation to find z:

8(9) + 6(-28/3) - z = 10

72 - 56 - z = 10

z = 6

The solution to the system is x = 9, y = -28/3, and z = 6.

Remember, always check the answer by substituting back into the original equations to ensure they are satisfied.

Question - Solve The Following System Of Equations For All Three Variables. 8x + 6y – Z = 10 –7x – 3y + Z = 5 4x + 3y + Z = 8