Question

Determine the number of solutions of the system of linear equations without writing the equations in slope intercept form. Explain.

Answer 1

what class is this?

Answer 2

Algebra 1

Answer 3

Do you have specific actual equations for this problem, or is it just a general question about how you would determine the number of solutions?

Answer 4

If you try to solve a system of linear equations and you get a solution like x = 2, y = 4 or something, then it has a single unique solution... this is the intersection point between the two lines that are the original equations.

If you try to solve and you can't solve and you get something like 5 = 5 or x = x, then it means the two line equations are actually just the same line, and it has infinitely many solutions.

If you try to solve and get nonsense like 2 = 4, then it means the lines are parallel and there are zero solutions.

Answer 5

THIS IS THE EQUATION

Answer 6

(oops caps)

Answer 7

@JakeV8

Answer 8

Do you see how the bottom equation is just twice the top equation? Every number is just multiplied by 2. That means it really is the same line... so the "solution" is every point on the line, or in other words, there are infinite solutions.

Answer 9

Ok I got you! thanks!

Answer 10

glad to help :)

An example of a parallel system would look like:

2x + y = 5
2x + y = 10

If you tried to solve, you wouldn't get a nice answer :) It might look like 5 = 10. The problem is that the slopes are the same, but the intercepts are different, and the lines are parallel, meaning they don't cross, so zero solutions.

Answer 11

Oh...OK that helps alot.