Does the system of equations have no solution, one solution, or infinitely many solutions?
y = 2x – 3
y = –x + 3
the lines have different slopes, so they have to intersect.
one solution
To determine whether the system of equations has no solution, one solution, or infinitely many solutions, we can compare the coefficients of x and y in both equations.
Given:
Equation 1: y = 2x - 3
Equation 2: y = -x + 3
Comparing the coefficients of x in both equations, we have:
Equation 1: Coefficient of x = 2
Equation 2: Coefficient of x = -1
Since the coefficients of x do not match, the system of equations does not have a unique solution.
To determine whether the system has infinitely many solutions or no solution, we can compare the ratios of the coefficients of x and y.
The ratio of the coefficients of x in Equation 1 and Equation 2 is -2/1 = -2.
The ratio of the coefficients of y in Equation 1 and Equation 2 is 1/1 = 1.
Since the ratios of the coefficients of x and y do not match, the system of equations does not have infinitely many solutions.
Therefore, the system of equations has NO SOLUTION.
To determine whether the system of equations has no solution, one solution, or infinitely many solutions, we should try to solve the equations simultaneously.
Given the system of equations:
y = 2x – 3 ...(Equation 1)
y = –x + 3 ...(Equation 2)
To solve the system, we can equate the two equations by setting the right sides equal to each other:
2x - 3 = -x + 3
We can then simplify the equation:
2x + x = 3 + 3
3x = 6
x = 2
Now, substitute the value of x = 2 into either equation (Equation 1 or Equation 2):
y = 2(2) – 3
y = 4 - 3
y = 1
Thus, we have x = 2 and y = 1, which gives us a unique solution for the system of equations.
Therefore, the system of equations has one solution.