x - 3y =-2
-3x +9y =2
Multiply the 1st equation by -3 and you have
-3x+9y = 6
-3x+9y = 6
So, both equations describe the same line. Any solution to one is also a solution of the other.
You are trying to solve two equations which are represented
by two parallel lines. There will be no solution, since parallel
lines will never intersect.
Here is what will happen:
multiply the first by 3, then add them
3x - 9y = 6
-3x + 9y = 2
0 = 2
this is a false statement.
If in solving 2 equations of this type, the variables drop out ....
1. you end up with a false statement, like ours above, there will
be no solution.
2. you end up with a true statement, then the two equations are
really just the same line, and there will be an infinite number of
solutions.
Looks like both Steve and me both made silly
arithmetic errors.
My answer to the addition should have been
0 = 8 , but the conclusion and what follows is still valid.
You mean 2 ≠ 9 ?
Dang!
To solve this system of equations, you can use the method of substitution or the method of elimination. I will demonstrate the method of substitution:
1. Start with the first equation: x - 3y = -2.
2. Solve this equation for x in terms of y by adding 3y to both sides: x = 3y - 2.
3. Now substitute this expression for x into the second equation: -3(3y - 2) + 9y = 2.
4. Simplify the equation by distributing the -3: -9y + 6 + 9y = 2.
5. Combine like terms: -9y + 9y + 6 = 2.
6. Simplify further: 6 = 2.
In step 6, we find that 6 is not equal to 2. This indicates that the system of equations is inconsistent, meaning there is no solution that satisfies both equations simultaneously. The lines represented by the equations are parallel and will never intersect.
Therefore, the system of equations is inconsistent and does not have a solution.