Final answer:
This solution involves solving a system of linear equations using the elimination method by creating additive inverses for the x-coefficients, allowing us to find the values of x and y.
Step-by-step explanation:
The question revolves around solving a system of linear equations in two variables using the method of elimination. The first step in solving the system consisting of Equation 1: 5x – 2y = -11 and Equation 2: –2x + 5y = 17 is to manipulate the equations so that either the x or the y coefficients are opposites, allowing them to be eliminated when the equations are added together.
To create additive inverses for the x-coefficients, we can multiply Equation 1 by 2 and Equation 2 by 5, which then allows us to add the two equations together to eliminate the x terms and solve for y. Once we find y, we can substitute it back into either Equation 1 or Equation 2 to solve for x, thus finding the solution to the system.