Solve the following system of equations.
x1 + 2x2 + 6x3 = 8
x1 + x2 + 3x3 = 4
see my previous reply to your same question.
Btw, you posted the same question just a few minutes apart. Patience is a virtue.
To solve the system of equations, we can use the method of elimination or substitution.
Let's use the method of elimination to solve this system of equations.
Step 1: Multiply equation 2 by -1 and add it to equation 1 to eliminate x1.
-1 * (x1 + x2 + 3x3) = -1 * 4
This gives us: -x1 - x2 - 3x3 = -4
Now let's add this to equation 1:
(x1 + 2x2 + 6x3) + (-x1 - x2 - 3x3) = 8 - 4
Simplifying, we get: x2 + 3x3 = 4
Now we have a new equation: x2 + 3x3 = 4. This will be equation 3.
Step 2: Subtract equation 2 from equation 3 to eliminate x2.
(x2 + 3x3) - (x2 + x3) = 4 - 4
Simplifying, we get: 2x3 = 0
Now we have a new equation: 2x3 = 0. This will be equation 4.
Step 3: Solve equation 4 for x3.
Dividing both sides of the equation by 2, we get: x3 = 0
Step 4: Substitute the value of x3 into equation 3 to solve for x2.
Substituting x3 = 0 into x2 + 3x3 = 4, we get: x2 + 3(0) = 4
Simplifying, we get: x2 = 4
Step 5: Substitute the values of x2 and x3 into equation 1 to solve for x1.
Substituting x2 = 4 and x3 = 0 into x1 + 2x2 + 6x3 = 8, we get: x1 + 2(4) + 6(0) = 8
Simplifying, we get: x1 + 8 = 8
Subtracting 8 from both sides of the equation, we get: x1 = 0
Therefore, the solution to the system of equations is:
x1 = 0
x2 = 4
x3 = 0