The given system consists of equations of planes. Notice that the coefficient of y in the first equation is the additive inverse of the coefficient of y in the second equation; they will add to be 0. Let's use the Elimination Method to find a solution to this system.
⎩⎪⎪⎨⎪⎪⎧3x−y+z=3x+y+2z=4x+2y+z=4(I)(II)(III)
We can start by adding the first equation to the second equation to eliminate the y-terms.
Having eliminated the y-variable from the second equation, we can continue by creating additive inverse coefficients for y in the first and third equations. Then, we can add or subtract these equations to eliminate y from the first equation.
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