How many solutions does the system have?
12x−15y=18
4x−5y=6 (1 point)
Responses
two solutions
two solutions
no solution
no solution
infinitely many solutions
infinitely many solutions
one solution
Make shore is correct
The correct answer is one solution.
To determine the number of solutions of the system of equations given, we can use the method of elimination.
First, let's write the system of equations:
12x - 15y = 18 (Equation 1)
4x - 5y = 6 (Equation 2)
To eliminate one of the variables, we can multiply both sides of Equation 2 by 3:
3(4x - 5y) = 3(6)
12x - 15y = 18 (Equation 3)
Now, we can compare Equation 1 and Equation 3:
Equation 1: 12x - 15y = 18
Equation 3: 12x - 15y = 18
We can see that both equations are identical. This means that the two equations represent the same line when graphed on the coordinate plane.
Therefore, the system of equations has infinitely many solutions.
To determine how many solutions a system of equations has, you can use either the substitution method, elimination method, or graphing method. Let's use the elimination method to solve the given system of equations.
Given system of equations:
1) 12x - 15y = 18
2) 4x - 5y = 6
To solve the system using the elimination method, we can multiply equation 2 by 3 to make the coefficients of y in both equations the same:
3 * (4x - 5y) = 3 * 6
12x - 15y = 18
Now, we have the same first equation as equation 1. Therefore, the system is dependent or consistent. It means that the equations represent the same line, and there are infinitely many solutions.
Hence, the system of equations has infinitely many solutions.