Final answer:
In the given system of equations, elimination is the most efficient method due to the coefficients of y being easily matched when one equation is multiplied by 2.
Step-by-step explanation:
To determine whether substitution or elimination is the most efficient method of solving the system of equations:
Elimination is generally preferred when you can easily eliminate one of the variables by multiplying the equations by suitable numbers and then subtracting them. Substitution is often used when one of the equations is already solved for one of the variables, making it easy to substitute the value into the other equation.
In this case, neither equation is solved for a single variable, and the coefficients of the variables are not convenient for straightforward elimination. However, if we multiply the first equation by 2, we create an equation with 4y, which is present in the second equation. This will allow us to eliminate y by subtracting.
Steps for elimination could include:
Multiply the first equation by 2.Subtract the new first equation from the second equation to eliminate y.Solve for the remaining variable (x).Substitute the value of x into one of the original equations to solve for y.
In this system of equations, elimination would be the most efficient method due to the coefficients of y being easily matched.