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Simplifying 30xm + 15xn + -20ym + -10yn = 0 Reorder the terms: 30mx + -20my + 15nx + -10ny = 0 Solving 30mx + -20my + 15nx + -10ny = 0 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-15nx' to each side of the equation. 30mx + -20my + 15nx + -15nx + -10ny = 0 + -15nx Combine like terms: 15nx + -15nx = 0 30mx + -20my + 0 + -10ny = 0 + -15nx 30mx + -20my + -10ny = 0 + -15nx Remove the zero: 30mx + -20my + -10ny = -15nx Add '10ny' to each side of the equation. 30mx + -20my + -10ny + 10ny = -15nx + 10ny Combine like terms: -10ny + 10ny = 0 30mx + -20my + 0 = -15nx + 10ny 30mx + -20my = -15nx + 10ny Reorder the terms: 30mx + -20my + 15nx + -10ny = -15nx + 15nx + 10ny + -10ny Combine like terms: -15nx + 15nx = 0 30mx + -20my + 15nx + -10ny = 0 + 10ny + -10ny 30mx + -20my + 15nx + -10ny = 10ny + -10ny Combine like terms: 10ny + -10ny = 0 30mx + -20my + 15nx + -10ny = 0 Factor out the Greatest Common Factor (GCF), '5'. 5(6mx + -4my + 3nx + -2ny) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(6mx + -4my + 3nx + -2ny)' equal to zero and attempt to solve: Simplifying 6mx + -4my + 3nx + -2ny = 0 Solving 6mx + -4my + 3nx + -2ny = 0 Move all terms containing m to the left, all other terms to the right. Add '-3nx' to each side of the equation. 6mx + -4my + 3nx + -3nx + -2ny = 0 + -3nx Combine like terms: 3nx + -3nx = 0 6mx + -4my + 0 + -2ny = 0 + -3nx 6mx + -4my + -2ny = 0 + -3nx Remove the zero: 6mx + -4my + -2ny = -3nx Add '2ny' to each side of the equation. 6mx + -4my + -2ny + 2ny = -3nx + 2ny Combine like terms: -2ny + 2ny = 0 6mx + -4my + 0 = -3nx + 2ny 6mx + -4my = -3nx + 2ny The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined.
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