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Mathematics

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To solve this system of equations, we can use the method of elimination or substitution. Here, I will show you the elimination method.

First, let’s eliminate the variable . We can do this by multiplying the second equation by and the third equation by , and then adding them to the first equation. This will eliminate :

Simplifying, we get:

Combining like terms, we have:

Next, let’s eliminate the variable . We can do this by multiplying the first equation by and the third equation by , then adding them to the second equation:

Simplifying, we get:

Combining like terms, we have:

Now we have two equations:

To eliminate the variable , let’s multiply the first equation by and the second equation by , then subtract the equations:

Simplifying, we get:

Combining like terms, we have:

Now we have two equations:

To eliminate the variable , let’s multiply the second equation by and the first equation by , then subtract the equations:

Simplifying, we get:

Combining like terms, we have:

Now we have two equations:

We can solve for in the first equation:

Substituting this into the second equation, we get:

Simplifying this expression, we get:

Combining like terms, we have:

To solve for , we can divide this equation by :

Finally, we can substitute the values of and back into any of the original equations to solve for . Let’s use the first equation:

After simplifying and solving for , we find:

Substituting this value back into the equation for , we get:

And substituting the values of and back into the equation for , we get:

Therefore, the solution to the system of equations is:

, ,

First, let’s eliminate the variable

Simplifying, we get:

Combining like terms, we have:

Next, let’s eliminate the variable

Simplifying, we get:

Combining like terms, we have:

Now we have two equations:

To eliminate the variable

Simplifying, we get:

Combining like terms, we have:

Now we have two equations:

To eliminate the variable

Simplifying, we get:

Combining like terms, we have:

Now we have two equations:

We can solve for

Substituting this into the second equation, we get:

Simplifying this expression, we get:

Combining like terms, we have:

To solve for

Finally, we can substitute the values of

After simplifying and solving for

Substituting this value back into the equation for

And substituting the values of

Therefore, the solution to the system of equations is: