Answer:
(3, 7)
Explanation:
To determine the solution of a system using a graph, we need to know the specific equations that make up the system. Generally, a system of equations consists of two or more equations with the same variables. Solving the system means finding the values of the variables that satisfy all the equations simultaneously.
In the given image, we are asked to consider a system of two linear equations in two variables, x and y:
Equation 1: y = -(2/3)x + 0
Equation 2: y = (13/3)x - 6
To solve this system graphically, you would plot both equations on the same graph. Where each equation represents a straight line, and the point where the lines intersect is the solution to the system, as it satisfies both equations simultaneously.
Thus, we can conclude after plotting both equations, that the solution that satisfies the system of equations is (3, 7).
Terminology:
System of Equations: A set of two or more equations with the same variables.
Linear Equations: Equations whose graphs form straight lines. They have the general form: y = mx + b, where m is the slope of the line, and b is the y-intercept.
Variables: Symbols (usually letters) that represent unknown quantities in an equation.
Solution to a System: The values of the variables that satisfy all the equations in the system.
Graphical Method: A method of solving a system of equations by plotting their graphs on the same coordinate plane.