Answer: x=-3, y=-4
Explanation:
System of equations is actually pretty simple.
Let me explain the two methods of solving a system of equations problem.
1. Elimination method
y-2x=2
-y=-x+1
In this approach, we will subtract or add the two equations together to eliminate one variable.
So in this problem, we'll organize -y=-x+1 like this:
x-y=1
Now we have
-2x+y=2
x-y=1
All we have to do now is add the two equations together and:
-x=3
x=-3
As you can see, the y variable is gone and we can find x by simply solving the rest.
Now we know that x=-3, let's plug in the value to get y.
x-y=1
-3-y=1
-y=4
y=-4
Therefore, x=-3, and y=-4
2. Substitution method
Let's go back to the problem.
y-2x=2
-y=-x+1
Now let's say that we will solve the problem using the substitution method.
In this approach, we will express one variable with the other.
So what we do is express y with x:
-y=-x+1
y=x-1
Now that we went through that process, we can plug in the y in the other equation:
x-1-2x=2
-x-1=2
-x=3
x=-3
Now that we now x=-3, let's plug that in to get y.
y=-3-1
y=-4
So the answer: x=-3, y=-4
Do you see the pattern?
System of equations problems are all about eliminating one variable and using the value of one to find the other.
Please let me know if there is anything else you're confused about.
Good luck with your exams!