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Solve the system of equations by elimination.\newline3x+3y−2z=−143x + 3y - 2z = -14\newlinex−y+2z=20x - y + 2z = 20\newline3x+y−3z=−153x + y - 3z = -15

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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.\newline3x+3y−2z=−143x + 3y - 2z = -14\newlinex−y+2z=20x - y + 2z = 20\newline3x+y−3z=−153x + y - 3z = -15
  1. Combine Equations to Eliminate zz: First, let's eliminate zz from the first and third equations by adding them.\newline3x+3y−2z=−143x + 3y - 2z = -14\newline3x+y−3z=−153x + y - 3z = -15\newlineAdd the equations:\newline(3x+3y−2z)+(3x+y−3z)=−14+(−15)(3x + 3y - 2z) + (3x + y - 3z) = -14 + (-15)\newline6x+4y−5z=−296x + 4y - 5z = -29
  2. Multiply and Add Equations to Eliminate zz: Now, let's eliminate zz from the second and third equations by multiplying the second equation by 33 and adding it to the third equation.\newline3(x−y+2z)=3(20)3(x - y + 2z) = 3(20)\newline3x−3y+6z=603x - 3y + 6z = 60\newlineNow add this to the third equation:\newline(3x−3y+6z)+(3x+y−3z)=60+(−15)(3x - 3y + 6z) + (3x + y - 3z) = 60 + (-15)\newline6x−2y+3z=456x - 2y + 3z = 45
  3. Subtract Equations to Eliminate xx: We now have two new equations without zz:6x+4y−5z=−296x + 4y - 5z = -296x−2y+3z=456x - 2y + 3z = 45Let's eliminate xx by subtracting the second equation from the first.(6x+4y)−(6x−2y)=−29−45(6x + 4y) - (6x - 2y) = -29 - 456x+4y−6x+2y=−746x + 4y - 6x + 2y = -746y=−746y = -74y=−746y = \frac{-74}{6}y=−12.333y = -12.333

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