How many solutions does the system have?
12x−15y=18
4x−5y=6 (1 point)
Responses
two solutions
two solutions
one solution
one solution
no solution
no solution
infinitely many solutions
one solution
To determine the number of solutions for the given system of equations:
12x - 15y = 18
4x - 5y = 6
We can use the method of solving systems of equations, such as substitution or elimination.
Using the elimination method, we can multiply the second equation by 3 to make the coefficients of x the same in both equations:
12x - 15y = 18
12x - 15y = 18
By subtracting the first equation from the second equation, we get:
0 = 0
This means that the two equations are equivalent, and any value of x and y that satisfies the first equation will also satisfy the second equation.
Hence, there are infinitely many solutions for this system of equations.
To determine the number of solutions in the given system of equations, we can use the method of solving using elimination or substitution. Let's solve it using elimination:
Given system of equations:
12x - 15y = 18
4x - 5y = 6
To eliminate the variable 'x', we need to manipulate the equations such that the coefficients of 'x' in both equations have the same value, or multiples of each other. By multiplying the second equation by 3, we can achieve this:
12x - 15y = 18
12x - 15y = 18
Now, when we compare the two equations, we can see that they are identical. This means that the two equations represent the same line on the coordinate plane, resulting in infinitely many solutions.
Therefore, the given system of equations has infinitely many solutions.