Sikve the following by using substitution method
x=3y -5
6x-18y = -30
I got this far and I'm stuck
6(3y-5) - 18y = -30
18y - 30 - 18y = -30
-30 = -30
So this doesn't make sense anymore
you did nothing wrong.
Notice that if you divide your second equation by 6 , you get
x - 3y = -5, which is really the same as your first equation.
So you were actually only given one equation twice.
In general, if you solve using proper algebra and your variables disappear, one of two things can happen
1. the resulting statement is TRUE.
in that case, there will be an infinite number of correct solutions. This is your case
2. the resulting statement in FALSE.
in that case there is no solution.
So your pair of equations have an infinite number of solutions, just form a table of values for
x = 3y - 5 to get a few of them if you have to
So some possible answers would be:
(13,6)
(22,9)
etc:
is that correct then?
To solve the given system of equations using the substitution method, follow these steps:
1. Start with equation 1: x = 3y - 5.
2. Substitute equation 1 into equation 2, replacing x with (3y - 5):
6(3y - 5) - 18y = -30.
3. Simplify the equation by distributing and combining like terms:
18y - 30 - 18y = -30.
This equation simplifies to -30 = -30.
4. Notice that we obtained a true statement (-30 = -30) rather than a false statement.
This means that the equations in the system are dependent, and all values of x and y will satisfy both equations.
In this case, the given system represents a dependent system, meaning there are infinitely many solutions. The equations represent the same line on a graph, and every point on that line constitutes a solution to the system.