A system of equations is a collection of two or more equations.
The solution to a system of equations in two variables is the pair of values that make both equations true.
A system can be solved graphically or algebraically. To solve a system graphically, graph both equations on the same coordinate plane and find the point of intersection. This point is the solution because it is the point that lies on both lines. This ordered pair (x, y) will make both equations true.
When solving real-world systems of equations, follow these steps:
Step 1: Identify critical information.
Step 2: Create two equations.
Step 3: Write the equations in slope-intercept form y = mx + b.
Step 4: Graph equations to determine the point of intersection.
Step 5: Analyze the answer.
A solution is viable if it makes sense and works consistently. A solution must answer the question being posed in the problem.
There are three types of systems of equations: