You can represent the factor by which the student multiplies the second equation by a third variable. Then you can check all the options if they're correct or not by the method shown below.
The equation that can be used by the student is
Option D: 20x + 18y = 76
Choose yes in this option and choose no for rest of the options.
How to find which equation is replaced by second equation to give same solution and that equation should be made by adding the first equation with multiple of second equation?
Let the multiple by which second equation is multiplied be "a".
Then we should have the new equation as:
[tex](12x + 8y) + a(4x + 5y) = 40 + a \times 18\\or\\(12+4a)x + (8 + 5a)y = 40 + 8a[/tex]
Now we will do trial and error. Since the x coefficient in the options are of only 2 types(12 and 20), we will try them first for less amount of trial and error.
Coefficient of x in new equation being 12:
Then we have:
[tex]12 + 4a = 12\\4a = 0\\a = 0[/tex]
Thus, new equation will be
[tex](12+4a)x + (8 + 5a)y = 40 + 8a\\(12+0)x + (8+0) = 40 _ 0\\12x + 8y = 40[/tex]
This is not given in option (and the fact that we don't multiply an equation by 0 as it will nullify the terms, and leave them useless)
Coefficient of x in new equation being 20:
Then we have:
[tex](12+4a)x = 20x\\12 = 4a = 20\\4a = 8\\a = 2[/tex]
Thus, new equation will be
[tex](12+4a)x + (8 + 5a)y = 40 + 18a\\(12 + 4 \times 2)x + (8 + 5 \times 2)y = 40 + 18 \times 2\\20x + 18y = 76[/tex]
The obtained new equation is present as the last option, thus, we have:
The equation that can be used by the student is
Option D: 20x + 18y = 76
Choose yes in this option and choose no for rest of the options.
Learn more about method of elimination here:
https://brainly.com/question/20385690
