Question

PLEASE PLEASE PLEASE HELP ME WITH ALGEBRA 1 PLEASE!?!?!?!?!!!?!?!?!?!?! I WILL GIVE LOTS OF POINTS AND BRAINLEST PLEEEEEEEEEEEEEEEEASE!!?!?!?!?!?!!?!?!?!?
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.

Answer 1

Answer:

• there are no solutions (lines do not intersect)
• 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. (No points will be on all the lines.)
• The lines may intersect at one point.
• The lines may be the same line, overlapping, identical, coincident, consisting of all the same points, an infinite number.