Question

Suppose a friend does not know which method would be most efficient for solving this system. x – 2y = -6 2x + y = 8 • Write a "note" to your friend explaining which method (substitution, elimination, graphing) would be most efficient and why. • Solve the system showing all work.

Answer 1

The most efficient method to solve the given system of equations x - 2y = -6 and 2x + y = 8 is the elimination method, resulting in the solution x = 2 and y = 4.

Step-by-step explanation:

Hi friend, when solving the system of equations:

• x – 2y = -6
• 2x + y = 8,

I would suggest using the elimination method because one equation can be easily manipulated to cancel out one of the variables when added to the other equation. Here are the steps to solve it:

1. Multiply the second equation by 2 to get 4x + 2y = 16. This allows the y variables to cancel out when added to the first equation.
2. Add the first equation to the new version of the second equation (x - 2y + 4x + 2y = -6 + 16) to get 5x = 10.
3. Divide both sides by 5 to solve for x. This gives us x = 2.
4. Now substitute x = 2 into one of the original equations to find y. Let's use the second equation: 2(2) + y = 8 turns into 4 + y = 8.
5. Subtract 4 from both sides to solve for y, which gives us y = 4.

So, the solution to the system is x = 2 and y = 4.