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Question 624402: Solve using the substitution method. Show your work. If the system has no solution or an infinite number of solutions, state this.
-x-3y=.20
5x+3y=40
Answer by math-vortex(648)   (Show Source):
You can put this solution on YOUR website!
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
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