The equations at the beginning are wrongly stated. They should be:
2x/5+4y/7=8
3x/8+5y/6=12
(The second variable doesn’t need to be y—it can be any variable other than x.)
This is because in a system of equations which can be solved uniquely there must be as many unknowns as there are equations. If x is the only unknown (as presented in the given two equations) only one equation would be needed to find x. Each of the given equations would give a different value for x when solved, so one or both equations would be false. With two unknowns, x and y, the system can be solved uniquely (one value for x and one for y).
So using the revised equations above, we multiply the first by 35 (the LCD of 5 and 7):
14x+20y=280, 7x+10y=140, 10y=140-7x, y=(140-7x)/10 is one substitution that could be used;
and the second by 24 (LCD of 8 and 6):
9x+20y=288, 20y=288-9x, y=(288-9x)/20 is another substitution that could be used.
Two of the answer options are correct.
Either substitution is correct. The idea in solving systems of equations is to reduce the system eventually to a single equation with a single unknown. Then solve for the unknown, and use the value to find the remaining unknown(s). There are always a number of different ways of solving simultaneous equations, and all are equally valid, although some methods may be faster than others.
