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?

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?

anonymous · Answer

(A) Show that the solution to the system of equations 3x + y = 5 and 8x –7y = 6 is the same as the solution to the given system of equations
(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
(C) Show that the solution to the system of equations 15x + 13y = 17 and 7x – 8y = 6 is the same as the solution to the given system of equations
(D) Show that the solution to the system of equations –13x + 15y = 17 and 7x – 8y = 6 is the same as the solution to the given system of equations

anonymous · Answer

@paki I think the answer is either B or D. Can you confirm plz?

anonymous · Answer

@dan815 @TheSmartOne

nincompoop · Answer

THINK? HOW ABOUT YOU SOLVE IT

anonymous · Answer

I did solve it on paper and pencil

nincompoop · Answer

show your solution

anonymous · Answer

Here let me show you why

anonymous · Answer

Because the directions said "equation 2 is kept unchanged and equation 1 is replaced with the sum of equation 1 and a multiple of equation 2," it means that you add x + 3y = 5      (equation 1) and 7x – 8y = 6     (equation 2) together. You will get 8x -5y = 11

anonymous · Answer

And then the directions say, "equation 2 is multiplied by 1." Multiplying equation 2 by 1 will leave it the same: 7x – 8y = 6

nincompoop · Answer

what is equation 1 is replaced with sum of equation 1?

anonymous · Answer

^equation 1 is replaced with the sum of equation 1 and a multiple of equation 2

anonymous · Answer

will be 8x -5y = 11

nincompoop · Answer

can you rewrite that in equation

nincompoop · Answer

where is the "multiple"

anonymous · Answer

The multiple of equation 2, I am assuming, is the same as equation 2: 7x – 8y = 6

anonymous · Answer

x + 3y = 5
7x – 8y = 6
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8x - 5y = 11