# SOLUTION: Plsss solve the System... thanx..... x + y + z - 2w = -4 2y + z + 3w = 4 2x+ y - z + 2w = 5 x - y + w = 4

Algebra ->  Algebra  -> Finance -> SOLUTION: Plsss solve the System... thanx..... x + y + z - 2w = -4 2y + z + 3w = 4 2x+ y - z + 2w = 5 x - y + w = 4      Log On

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 Click here to see ALL problems on Finance Question 447917: Plsss solve the System... thanx..... x + y + z - 2w = -4 2y + z + 3w = 4 2x+ y - z + 2w = 5 x - y + w = 4Answer by Edwin McCravy(8924)   (Show Source): You can put this solution on YOUR website!``` x + y + z - 2w = -4 2y + z + 3w = 4 2x + y - z + 2w = 5 x - y + w = 4 z is already eliminated in the 4th equation, Add the 1st and 3rd equation to eliminate z x + y + z - 2w = -4 2x + y - z + 2w = 5 --------------------- 3x + 2y = 1 Add the 2nd and 3rd equation to eliminate z 2y + z + 3w = 4 2x + y - z + 2w = 5 --------------------- 2x + 3y + 5w = 9 So now we have this system of equations in only x, y, and w. Not z: x - y + w = 4 3x + 2y = 1 2x + 3y + 5w = 9 w is already eliminated from the 2nd equation, so multiply the 1st equation by -5 and add it to the 3rd equation: -5x + 5y - 5w = -20 2x + 3y + 5w = 9 ------------------- -3x + 8y = -11 So now we have this system of equations in only x and y. Not z or w: 3x + 2y = 1 -3x + 8y = -11 ---------------- 10y = -10 y = -1 Substitute y = -1 in 3x + 2y = 1 3x + 2(-1) = 1 3x - 2 = 1 3x = 3 x = 1 Substitute x = 1 and y = -1 in x - y + w = 4 1 - (-1) + w = 4 1 + 1 + w = 4 2 + w = 4 w = 2 Substitute x = 1, y = -1, and w = 2 in x + y + z - 2w = -4 1 + (-1) + z - 2(2) = -4 1 - 1 + z - 4 = -4 z - 4 = -4 z = 0 (x,y,z,w) = (1,-1,0,2) Edwin```