In Exercises 61–66, find the solution set for each system by graphing both of the system's equations in the same rectangular coordinate system and finding points of intersection. Check all solutions in both equations.

Verified step by step guidance

1. Step 1: Identify the equations in the system.
2. Step 2: Rewrite each equation in slope-intercept form, $y=mx+b$, if necessary.
3. Step 3: Graph each equation on the same rectangular coordinate system.
4. Step 4: Identify the point(s) of intersection of the graphs.
5. Step 5: Check the solution(s) by substituting the point(s) of intersection back into the original equations to verify they satisfy both equations.

Key Concepts

Systems of Equations

A system of equations consists of two or more equations with the same variables. The solution to the system is the set of values that satisfy all equations simultaneously. In graphical terms, this means finding the points where the graphs of the equations intersect, which represent the common solutions.

Graphing Linear Equations

Graphing linear equations involves plotting points that satisfy the equation on a coordinate plane. Each equation can be represented as a line, and the slope-intercept form (y = mx + b) is commonly used to identify the slope and y-intercept. Understanding how to graph these lines accurately is crucial for visualizing the solution set of a system.

Checking Solutions

After identifying potential solutions from the graph, it is essential to verify these solutions by substituting them back into the original equations. This step ensures that the points of intersection indeed satisfy both equations, confirming their validity as solutions to the system.