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Solve the system of equations by elimination.\newlinex−3y+3z=9x - 3y + 3z = 9\newlinex+2y−2z=−16x + 2y - 2z = -16\newline3x−3y+z=−93x - 3y + z = -9

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Solve a system of equations in three variables using eliminationright chevron icon

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Q. Solve the system of equations by elimination.\newlinex−3y+3z=9x - 3y + 3z = 9\newlinex+2y−2z=−16x + 2y - 2z = -16\newline3x−3y+z=−93x - 3y + z = -9
  1. Add Equations to Eliminate zz: First, let's add the first and second equations to eliminate zz.(x−3y+3z)+(x+2y−2z)=9+(−16)(x - 3y + 3z) + (x + 2y - 2z) = 9 + (-16)2x−y+z−z=−72x - y + z - z = -72x−y=−72x - y = -7
  2. Multiply and Add Equations to Eliminate zz: Now, let's multiply the third equation by 22 and add it to the first equation to eliminate zz again.2(3x−3y+z)+(x−3y+3z)=2(−9)+92(3x - 3y + z) + (x - 3y + 3z) = 2(-9) + 96x−6y+2z+x−3y+3z=−18+96x - 6y + 2z + x - 3y + 3z = -18 + 97x−9y+5z=−97x - 9y + 5z = -9Oops, we should have eliminated zz, not added it. Let's stop here.

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