Which describes the system of equations below?
y= 4x -4/9
y= 7/2x +3/7
y
=
–10
7
x
+
3
7
y
=
–10
7
x
−
7
8
The system of equations can be described as a set of two linear equations. In order to determine their characteristics and relationship, we will explain how to analyze the system of equations.
First, let's write down the given equations:
Equation 1: y = 4x - (4/9)
Equation 2: y = (7/2)x + (3/7)
To describe the system of equations, we will focus on the coefficients of x and y, as well as the constants.
For Equation 1, the coefficient of x is 4, and the constant term is -(4/9).
For Equation 2, the coefficient of x is 7/2, and the constant term is 3/7.
Now, let's analyze the system of equations:
1. Consistency: To determine if the system is consistent (i.e., there is at least one solution), we compare the slopes (coefficients of x).
The slope of Equation 1 is 4, and the slope of Equation 2 is 7/2. Since the slopes are not equal, the lines represented by the equations are not parallel and will intersect at a single point. Therefore, the system is consistent.
2. Unique solution: To check if there is a unique solution (i.e., a single point of intersection), we can compare the coefficients of x and y.
The coefficients of x in the two equations are different, and the coefficients of y are also different. Thus, there is no common multiple between the coefficients of x or y. Consequently, there is a unique solution for this system.
In conclusion, the system of equations represents two non-parallel lines and has a unique solution.