solve the following systems of linear equations by graphing. graph equations.

Question

in your submitted answer, describe what the graph looks like, and what this tells you about the solution to this system of linear equations.
x + y= 3
6x = -6y + 18
a the lines are parallel. no solution.
b the lines intersect at 1 point. the solution is the point (0,3)
c the lines coincide. there are infinite solutions

Answer 1

To graph the system of equations:
1) x + y = 3 can be rewritten as y = -x + 3
2) 6x = -6y + 18 can be rewritten as y = -x + 3

Both equations have the same slope of -1, so the lines are parallel. When we graph the lines, we see that they are exactly on top of each other. This means that they coincide and have infinite solutions.

Therefore, the answer is:

c) the lines coincide. there are infinite solutions