PLEASE PLEASE PLEASE HELP ME WITH ALGEBRA 1 PLEASE!?!?!?!?!!!?!?!?!?!?! I WILL GIVE LOTS OF POINTS AND BRAINLEST PLEEEEEEEEEEEEE
EEEASE!!?!?!?!?!?!!?!?!?!? What are the different types of solutions that you can get when you solve a system of linear equations? Describe the graphs of these different types of systems.
there is one solution (lines intersect at one point)
there are an infinite number of solutions (lines overlap—are the same line)
Step-by-step explanation:
"A system of linear equations" covers a lot of territory. In Algebra 1, it usually means two linear equations in two unknowns. Each of those equations will graph as a line on a coordinate plane.
A solution is a point that satisfies all the equations. That is, it is a point that is on all the lines described by the system of equations.
The geometry of lines on a plane comes into play with regard to solutions.
The lines may be parallel, hence never intersect. (<em>No points</em> will be on all the lines.)
The lines may intersect at <em>one point</em>.
The lines may be the same line, overlapping, identical, coincident, consisting of <em>all the same points, an infinite number</em>.
