Use parametric equations to describe the solution set of the

Use parametric equations to describe the solution set of the linear equation. 15x_1 - 4x_2 + 3x_3 = 6 Give the exact answer. Use fractions if necessary. x_1 = t X_2 = s x3(t, s) =

Solution

Given that

15x₁ - 4x₂ + 3x₃ = 6   x₁ = t , x₂ = s

3x₃ = 6 - 15x₁ + 4x₂

x₃ = ( 6 - 15x₁ + 4x₂ ) / 3

x₃ = ( 6 - 15t + 4s ) / 3

Therefore,

x₃( t , s ) = ( 6 - 15t + 4s ) / 3