Weby. Interpret your answers and draw the graph. Solution. The graph ofz= 1¡x¡1 2 yis a plane passing through the points (x;y;z) = (1;0;0), (0;2;0) and (0;0;1). The partial derivatives are: @z @x =¡1; @z @y =¡1 2 Webx + z =2y or x – 2y + z = 0 Solution: Given, x + y + z =6 y + 3z = 11 x + z =2y or x – 2y + z = 0 Let us write these equations in the form AX = B. [ 1 1 1 0 1 3 1 − 2 1] [ x y z] = [ 6 11 0] Now, D = A = 1 1 1 0 1 3 1 − 2 1 = 1 ( 1 + 6) − 1 ( 0 − 3) + 1 ( 0 − 1) = 7 + 3 − 1 = 9 D ≠ 0 so the given system of equations has a unique solution.
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WebOct 13, 2024 · -x + y - 2z = 0 Add this equation to the second equation = (x-2y+3z = - 1) + (-x + y - 2z = 0) = -y + z = -1 Multiply the first equation by -2= -2x+2y-4z = 0 Add this equation to the third equation = (-2x+2y-4z=0) + (2x-2y+z=1) = -3z = 1 z = - 1/3 (-y + z = - 1 ) = -y - 1/3 = -1 -1/3 + 1 = y y = 2/3 WebJul 17, 2024 · 2 x + y + 2 z = 10 x + 2 y + z = 8 3 x + y − z = 2 Solution We write the augmented matrix. [ 2 1 2 10 1 2 1 8 3 1 − 1 2] We want a 1 in row one, column one. This can be obtained by dividing the first row by 2, or interchanging the second row with the first. Interchanging the rows is a better choice because that way we avoid fractions. black whip it
Solve the system of equations, using matrix method x - y + z
WebTo solve a system of equations by elimination, write the system of equations in standard form: ax + by = c, and multiply one or both of the equations by a constant so that the … WebJan 19, 2016 · X+Y = 10 X+Z = 20 Y+Z = 24 Let's restate the first two equations Y = 10-X Z = 20-X And substitute these expressions of Y and Z in the 3rd equation (10-X) + (20-X) = 24 Now rearrange terms and solve for X -2X = 24-10-20 = -6 X = 3 Use this value of X to find Y and Z Y = 10-X = 10-3 = 7 Z = 20-X = 20-3 = 17 Since X = 3, Y = 7 and Z = 17 WebSolve for x, y, and z 1st Equation: 2x + 2y + 4z = 48 2nd Equation: 2x + 9y + 7z = 105 3rd Equation: x + 4y + z = 37 Subtract the 2nd Equation from the 1st Equation. This will eliminate the variable “x”. 2x + 2y + 4z = 48 - (2x + 9y + 7z = 105) ---------------------------- 0 - 7y - 3z = -57 -7y - 3z = -57 Solve for “z” in terms of y fox peak outdoor supply llc