Question

Based on the graph of the following system of equations, determine the number of solutions.

3x + 2y = 5
6y = 10 - 4x

Answer 1

I may not be much help here as I'm not sure what they mean by the number of solutions. Solving the system of equations I get a solution for x, which equals the solution for y. This may mean that there is only one solution, but again I'm not sure I understand the question. How I solved it is by solving 3x+2y=5 for y. y=(5-3x)/2 Then I substituted that into the second equation in place of y: 6*((5-3x)/2)=10-4x. Solving for x by multiplying (5-3x)/2 by 6 and moving the x's to one side and the numbers to the other you get 5=5x so x=1. Putting that into the solution for y gives y=(5-3(1))/2=2/2=1. So the solution for x is 1 and for y is 1. But i'm not sure that helps with the number of solutions question.

Answer 2

No solutions
Infinitely many solutions
Exactly two solutions
Exactly one solution

Answer 3

There is definitely a solution as we proved x=1 and y=1 is a solution. I don't know if that qualifies as one solution or two... I would think one. I'm sure there's a way to test it to verify but it's not coming to mind. If I were to guess I would say one solution, but don't base your answer on my guess...

Answer 4

yeah thats what i was getting to one solution okay thank you!