Question

How many solutions are there to the following system of equations?
6x+12y=11
4x+8y=3

A. infinitely many
B. 1
C. 0
D. 2

Answer 1

Have you tried finding the solutions? if there is any .

Answer 2

Do you know how to solve the system of equations?

If you can find the slope of both equations, you can compare the slopes. If the slopes are unequal, then the lines intersect, and there will be 1 solution. If the slopes are equal, then they may be coincident (infinitely many solutions) or parallel (no solutions). To determine which case you have, you have to find the \(y\)-intercept for each equation. If they are equal, you have coincident lines, otherwise parallel.

If you solve the system, you will get an answer which is either a single point (single solution), a true statement such as \(3 = 3\) (coincident, infinitely many solutions) or a false statement such as \(3 = 4\) (parallel, no solutions).

Answer 3

If you aren't comfortable finding the solution to the system, tell me and I will show you how to do it.