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You can put this solution on YOUR website!
\n" ); document.write( "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.
\n" ); document.write( "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.
\n" ); document.write( "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.
\n" ); document.write( "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.
\n" ); document.write( "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
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\n" ); document.write( "It turns out this path makes the solution VERY easy, because subtracting one of these equations from the other gives us y=1.
\n" ); document.write( "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. \n" ); document.write( "