Question

Here is a system of linear equations: 2x+1/2y=7 and 6x−1/2y=5. Which would be more helpful for solving the system: adding the two equations or subtracting one from the other? Explain your reasoning.

A. Adding the two equations, to eliminate the yy variable
B. Subtracting one equation from the other, to eliminate the x variable
C. Adding the two equations, to eliminate the x variable

D. Subtracting one equation from the other, to eliminate the y variable

Answer 1

The most effective method to solve the given system of linear equations is by adding the two equations together to eliminate the y variable, solve for x, and then substitute x back into one of the original equations to find y. The solution is x = 1.5 and y = 8.

Step-by-step explanation:

To solve the system of linear equations given by 2x+1/2y=7 and 6x−1/2y=5, it would be more helpful to add the two equations. This is because adding them will result in the y variable being eliminated, as the 1/2y in the first equation and the −1/2y in the second equation will cancel each other out. Once we do this, we can solve for x and then substitute that value back into one of the original equations to solve for y.

So, adding the two equations gives us:
2x + 1/2y + 6x - 1/2y = 7 + 5
8x = 12
Dividing both sides by 8 gives us x = 12/8 or x = 1.5.

Now, we can substitute x = 1.5 into one of the original equations to find y. Let's use the first equation:
2(1.5) + 1/2y = 7
3 + 1/2y = 7
1/2y = 4
y = 8.

Hence, the solution to the system of equations is x = 1.5 and y = 8.