I have to solve the system.
3x + y = 12
y = 9 - 3x
I used the substitution method to get
3x + 9 - 3x = 12
But now I'm stuck.
The system is indeterminate. THe two lines are parallel, and do not have a solution. Rearrange the second equation to
3x+y=9 Which is the same x,y coefficents as the first equation.
Solving a system of equations means finding the intersection of the two lines.
Your 2 equations represent two parallel lines, they cannot intersect, therefore you cannot have a solution.
To solve the system of equations using the substitution method, you are on the right track. Let's continue solving the equation you obtained:
3x + 9 - 3x = 12
When we combine like terms, we get:
9 = 12
However, this equation is not true. It means that the system of equations is inconsistent, which means there is no solution that satisfies both equations simultaneously.
In this case, the two lines representing the equations are parallel and will never intersect. Therefore, there is no common solution.
To solve the given system of equations using the substitution method, you've made a good start by substituting the value of y from the second equation into the first equation. Now, let's continue solving the equation.
After substituting y = 9 - 3x into the first equation, you get:
3x + (9 - 3x) = 12
Now, you can simplify the equation by combining like terms:
3x - 3x + 9 = 12
The variable x cancels out, leaving just the constant term:
9 = 12
From this equation, we can see that there is no value of x that satisfies the equation. Therefore, there is no solution to the system of equations.
When you encounter a situation where the equation leads to a false statement or an inconsistency (like 9 = 12 in this case), it means that the system of equations is inconsistent and has no solution.