Acopper alloy that is 40% copper is to be combined with a copper alloy that is 80% copper to produce 120 kilograms of an alloy that is 70% copper. how many kilograms of each alloy must be used? work it out

Try this way:
1. note, that in such tasks mass of pure copper before merging and after merging is the same (this is the base);
2. If the mass of pure copper in alloy with 40% solution is 'x' and the mass of pure copper in alloy with 80% solution is 'y', then It means before merging was x/0.4 and y/0.8, after merging was (x+y)/0.7. It is one equation of the future system.
3. Using 120 kg. of 70% solution, it is possible to define mass of pure copper after merging, 120*0.7(=84 kg.). And before merging it was 'x+y' kg. of pure copper. It is the second equation of the future system.
4. according to the items no.2&3 (to make up the system of two equations and solve it). All the details are in the attached picture.
5. pure copper in 40% solution is 12 kg., pure copper in 80% solution is 72 kg. It means, that the copper alloy with 40% solution is x:0.4=12/0.4=30 kg., and the copper alloy with 80% solution is y:0.8=72/0.8=90 kg.

4+2=-2. 1+2=3. y=-2/3x+b. 2=4/3+b. 2/3=b. the answer is y= -2/3x+2/3