Question 595695
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.<br>
Next we substitute for the "solved for" variable in the <i>other</i> 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<br>
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<br>
So the solution to the system is the single point (1/2, -1/2)