Solving Systems of Equations by Graphing

What is indicated when a system of two linear equations has no solution?

Which outcome is observed when two linear equations in a system share all values/points?

Which of the following statements is true about a system of equations that has a single solution?

Consider the following system of equations: $y = ax + b$ $y = cx + d$ Under what condition will this system have infinite solutions?

What does the solution to a system of two linear equations represent graphically?

Systems of Equations

Solution (System of Equations)

No Solution (System of Equations)

Infinite Solutions (System of Equations)

Systems of equations are two or more linear equations that work together.
They use the same variables, x and y, and are always grouped together.
Example of system of equations is y = 3x + 2 and y = 4x - 6.
With systems of equations, there can be up to three possible outcomes: solution, no solution, and infinite solutions.

Solution

Equations share 1 common value/point.
Lines intersect at one point.

No solution

Equations don't share a common value/point.
Lines are parallel.

Infinite solutions

Equations share all values/points.
Lines overlap on graph.

Graphing Systems - Solution

A solution means that you have found a value for x and y that work for both equations.
When graphing, the lines will intersect at the solution.
Equations will have different slopes.
A solution point means that both equations share the same x and y values at that point.
For the example equations y = 2x + 0 and y = 1x + 2, the solution is (2, 4)
The point (2, 4) is the point both lines share; when x = 2, both equations will have y = 4.

Learn how to identify solutions to systems of equations by graphing. A solution exists when lines intersect at a single point, representing shared x and y values. No solution occurs when lines are parallel, and infinite solutions when lines overlap.