Question 595695: Solve the equations by substitution. If the equations are inconsistent and the solution is an empty set, write "no solution".
3x - y = 2
y = x - 1
Answer by jsmallt9(3758)   (Show Source):
You can put this solution on YOUR website! 3x - y = 2
y = x - 1
The first part of the Substitution method is to solve one of the equations for one of the variables. ("Solve for a variable" means get that variable all by itself on one side of the equation.) Since the y in the second equation is already "solved for" we can proceed to the next step.
Next we substitute for the "solved for" variable in the other equation. So we will substitute for y in the other (i.e. first) equation:
3x - (x-1) = 2
Notice the use of parentheses. This is an extremely good habit whenever you make substitutions. In this case, with the minus in front of and the parentheses around x-1 we know that we should subtract both the x and the -1:
2x + 1 = 2
Now we solve for x. Subtracting 1 from each side we get:
2x = 1
Dividing by 2 we get:
x = 1/2
It is easy to think we're finished. But we only have half the answer. We also need the value for y. For this we substitute the value we got for x into wither one of the original equations. I'll pick the 2nd equation:
y = (1/2) - 1
(Parentheses!)
which simplifies to:
y = -1/2
So the solution to the system is the single point (1/2, -1/2)
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