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.
x²/25 + y²/9 = 1
y = 3

Verified step by step guidance

1. Identify the two equations in the system that you need to solve simultaneously.
2. Rewrite each equation in slope-intercept form, $y=\mathrm{mx}+b$, if they are not already, to make graphing easier.
3. Graph both equations on the same coordinate plane by plotting the y-intercept $b$ and using the slope $m$ to find additional points for each line.
4. Locate the point(s) where the two graphs intersect; these points represent the solution(s) to the system.
5. Substitute the coordinates of each intersection point back into both original equations to verify that they satisfy both equations, confirming the solution set.

Key Concepts

Systems of Equations

A system of equations consists of two or more equations with the same set of variables. The solution to the system is the set of values that satisfy all equations simultaneously. Understanding how to interpret and solve these systems is fundamental in algebra.

Graphing Linear Equations

Graphing involves plotting equations on a coordinate plane to visualize their solutions. For linear equations, this means drawing straight lines. The graph helps identify where the lines intersect, which corresponds to the solution(s) of the system.

Points of Intersection

The point(s) where two graphs meet represent the solution(s) to the system of equations. Each intersection point satisfies both equations. Checking these points by substituting back into the original equations ensures the solution's accuracy.