Decide if it is more convenient to solve the system of equations using substitution or elimination.

x=4y-3
4x-2y=-6
elimination substitution

1 answer

To determine whether substitution or elimination would be more convenient for solving the given system of equations, let's analyze the equations:

  1. \( x = 4y - 3 \) (Equation 1)
  2. \( 4x - 2y = -6 \) (Equation 2)

Substitution Method: Since Equation 1 already expresses \( x \) in terms of \( y \), the substitution method appears to be straightforward. You can substitute \( x \) from Equation 1 into Equation 2:

Substituting \( x = 4y - 3 \) into Equation 2 gives: \[ 4(4y - 3) - 2y = -6 \] This simplifies to a single variable equation that can be solved for \( y \).

Elimination Method: For the elimination method, we would typically want both equations in standard form. In this case, Equation 1 is already solved for \( x \), making it harder to eliminate one of the variables directly without rearranging both equations. We would need to express both in terms of \( x \) and \( y \), which complicates the elimination process.

Conclusion: Based on the analysis, it is more convenient to use the substitution method for this system of equations since one equation is already solved for \( x \), allowing for an easy substitution into the second equation.