Question

Solve by the linear combination method (with or without multiplication). x + y = 40 0.08x + 0.03y = 1.7

Answer 1

That's also known as the addition method.
   x + y = 40
.08x+.03y=1.7
We need to multiply the top equation by either a -.08 or a -.03 to eliminate one of the variables.  Let's get rid of the y:
-.03(x + y) = -.03(40) which gives us

-.03x - .03y = -1.2
 .08x + .03y = 1.7
When we add those together we are left with .05x = .5 and x = 10.  If we sub that 10 in for x into the first equation (either would have worked but the first one is way easier to work with!) we get 10 + y = 40 and y = 30.  So the solution to the system is (10, 30)