Solve the following system of equations by graphing. If the system is inconsistent or the equations are dependent, say so
5x-2y=3
10x-4y=6
I know the equations are dependent but I am confused on what is the solution set I'm thinking its (10x-4y=6) but I'm really not sure.
2 answers
if they are dependent they are the same line. So, the solution set is all real numbers. Any solution to one equation is a solution to the other.
Notice that when you double the first equation (line), you get the second equation.
Thus you have really one equation.
So there would be an infinite number of solutions, that is, any point on the line is a solution
If the second equation would have been
10x - 4y = 5, you would have two separate but parallel lines, which would never intersect.
In that case there would have been no solution.
Thus you have really one equation.
So there would be an infinite number of solutions, that is, any point on the line is a solution
If the second equation would have been
10x - 4y = 5, you would have two separate but parallel lines, which would never intersect.
In that case there would have been no solution.
2 answers