Tell whether the system has one solution, infinitely many solutions, or no solution. 9x+8y=15;9x+8y=30
The given system of equations is:
9x + 8y = 15 ...(1)
9x + 8y = 30 ...(2)
To determine whether the system has one solution, infinitely many solutions, or no solution, we can do a comparison of the equations.
The two equations are in the same form: 9x + 8y = c, where c = 15 for equation (1) and c = 30 for equation (2).
By comparing the coefficients of x and y, we can see that they are equal in both equations. This means that the lines represented by these equations are parallel since they have the same slope.
When two lines are parallel and have the same slope, they will never intersect, which implies that the system has no solution.
Thus, the given system of equations has no solution.
Tell whether the system has one solution, infinitely many solutions, or no solution.
5x-3y=10;10x+6y=20
The given system of equations is:
5x - 3y = 10 ...(1)
10x + 6y = 20 ...(2)
To determine whether the system has one solution, infinitely many solutions, or no solution, we can rearrange the equations to the slope-intercept form (y = mx + b).
Rearranging equation (1), we get:
-3y = -5x + 10
Dividing by -3, we have:
y = (5/3)x - (10/3)
Rearranging equation (2), we get:
6y = -10x + 20
Dividing by 6, we have:
y = (-5/3)x + (10/3)
By comparing the equations, we can see that the slopes of both lines are -(5/3), which means they are parallel.
However, the y-intercepts of the lines are different. The y-intercept of equation (1) is -(10/3) while the y-intercept of equation (2) is (10/3).
Since the lines are parallel and have different y-intercepts, they will never intersect. Therefore, the system has no solution.
Thus, the given system of equations has no solution.