Raphael graphed the system of equations shown. – Raphael graphed the system of equations shown, embarking on a journey to uncover the hidden solutions that lie within the intricate web of lines. This exploration delves into the realm of coordinate geometry, where equations take graphical form, revealing the secrets of their relationships.
In this captivating narrative, we will witness the transformation of algebraic expressions into visual representations, unraveling the mysteries of intersecting lines and their significance in solving systems of equations. Join us as we embark on this mathematical adventure, where the power of graphing unveils the harmony between equations and their solutions.
Raphael Graphed the System of Equations
Raphael graphed the system of equations shown. The system consists of two linear equations in two variables, x and y.
Equations Overview
The system of equations is as follows:
- y = 2x + 1
- y = -x + 3
Graphing the Equations
To graph each equation, Raphael plotted the intercepts and then drew a line through the points. The graph of y = 2x + 1 is a line with a y-intercept of 1 and a slope of 2. The graph of y = -x + 3 is a line with a y-intercept of 3 and a slope of -1.
Intersection Point, Raphael graphed the system of equations shown.
The two lines intersect at the point (1, 3). This point is the solution to the system of equations, because it satisfies both equations.
Solution Verification
To verify the solution, Raphael substituted the values of x and y into the original equations. He found that both equations were satisfied, so the solution is correct.
FAQ Resource: Raphael Graphed The System Of Equations Shown.
What is the significance of the intersection point in a system of equations?
The intersection point represents the solution to the system of equations, the values of the variables that satisfy both equations simultaneously.
Why is it important to verify the solution to a system of equations?
Verifying the solution ensures that the values obtained from the intersection point indeed satisfy both equations, confirming the accuracy of the solution.
