How many solutions does the system have?explain
-3x+6y=10
-3x+6y=-4
To determine how many solutions the system of equations has, we need to compare the coefficients of the variables. Looking at the system:
-3x + 6y = 10 (Equation 1)
-3x + 6y = -4 (Equation 2)
We can see that both equations have the same coefficients (-3 and 6) for the variables x and y. The only difference is the constant term on the right side of the equations.
Now, if the constant terms are different, such as in this case, 10 and -4, we can come to the conclusion that the two lines represented by these equations are parallel.
Parallel lines never intersect, which means they have no points in common. Therefore, the system of equations has no solution.
To determine the number of solutions a system of linear equations has, we need to analyze the coefficients of the variables and the constants in the equations. In this case, we have the following system of equations:
-3x + 6y = 10 (Equation 1)
-3x + 6y = -4 (Equation 2)
Let's first simplify both equations by dividing them by a common factor of -3:
Equation 1 becomes: x - 2y = -10/3
Equation 2 becomes: x - 2y = 4/3
Now, if we compare the simplified equations, we can see that the coefficients of x and y are the same in both equations, and the constants on the right side of the equations are different. This means that the two equations represent parallel lines.
When two lines are parallel, they never intersect, so there are no common solutions to the system. In other words, this system has no solution, or it is inconsistent.
Therefore, the system -3x + 6y = 10 and -3x + 6y = -4 has zero solutions.
none
how can -3x+6y be both 10 and 4?