Question 1134190
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There are always a huge number of different ways you could go about solving a system of equations like this.  Unless you have a huge amount of experience solving them, you don't know what paths are going to make the solution easy and which will make it a mess.<br>
The solution by tutor @MathLover1 starts by observing that the first and third equations have the same coefficients for x and z, so subtracting one equation from the other immediately allows you to solve for y.  But the path from there to the solution turns out to be a bit messy.<br>
Usually, with a system of three linear equations in three variables, you look for ways to eliminate one variable at a time.  The easiest variable to eliminate first is nearly always the one that has the "least complicated" coefficients in the three equations.<br>
In your example, with "-z" in two of the equations and "+z" in the other, the path to the solution is probably going to be easiest if we eliminate z first.<br>
So add the first and second equations to eliminate z, and do the same with the second and third equations.  The two resulting equations are<br>
{{{3x+y = 25}}}
{{{3x+2y = 26}}}<br>
It turns out this path makes the solution VERY easy, because subtracting one of these equations from the other gives us y=1.<br>
Then substituting y=1 in either of those two equations gives x=8; then substituting x=8 and y=1 in any of the original equations gives z=7.