Question

A system of equations is shown below: x + 3y = 5 (equation 1) 7x − 8y = 6 (equation 2) A student wants to prove that if equation 2 is kept unchanged and equation 1 is replaced with the sum of equation 1 and a multiple of equation 2, the solution to the new system of equations is the same as the solution to the original system of equations. If equation 2 is multiplied by 1, which of the following steps should the student use for the proof?

Answer 1

The correct answer is B. Show that the solution to the system of equations 8x − 5y = 11 and 7x − 8y = 6 is the same as the solution to the given system of equations"

Explanation:

Answer 2

(1) x + 3y = 5

(2) 7x - 8y = 6

Condition: equation (2) is multiplied by 1

If you multiply equation (1) by 1 and add the equation (2), you get

x + 3y = 5
7x - 8y = 6
----------------
8x - 5y = 11

So, if the student proves that the system formed by the new equation and the second equation is the same, he/she will have the proof:

So, the answer is "show that the solution to the system of equations 8x − 5y = 11 and 7x − 8y = 6 is the same as the solution to the given system of equations"