Hi, there-- The Problem: Solve this system of equations using the substitution method. -x-3y=.20 5x+3y=40 Solution: Rewrite the first equation in "x=..." form. -x-3y=0.20 -x=3y+0.20 x=-3y-0.20 We see that -3y-0.20 and x are equivalent. Make this substitution in the second equation. 5x+3y=40 5(-3y-0.20)+3y=40 Simplify the equation and solve for y. -15y-1+3y=40 -12y-1=40 -12y=41 y=-41/12 We know that y=-41/12. We'll keep this value as a fraction for now because it is more accurate than the decimal form. Substitute -42/12 for y in the second equation. 5x+3y=40 5x+3(-41/12)=40 Simplify and solve for x. 5x-41/4=40 5x=40+41/4 5x=201/4 x=(201/4)*(1/5) x=201/20 The solution to the system is the ordered pair (201/20,-41/12). We need to check this solution in the original equations. -x-3y=.20 -(201/20)-3(-41/12)=0.20 -201/20+123/12=0.20 (I didn't show all the arithmetic to get LCD=60, add, then reduce) 1/5=0.20 0.20=0.20 Check! 5x+3y=40 5(201/20)+3(-41/12)=40 1005/20-123/12=40 40=40 Check! Check! That's it. The solution is (201/20,-41/12). Just a note. This system would be much easier to solve with the elimination method. When you add together the original equations, the y-terms cancel out. Some times textbooks have you solve these the least efficient way (just to be evil, I guess!) However, when you have the choice, it's good to look for the most efficient method. Mathematicians are all about working smarter, not harder! Please email your questions/comments about the solution. I want to make sure you understand, and I'd appreciate the feedback. Ms.Figgy math.in.the.vortex@gmail.com