y = 3x + 6
y = -13x - 4
does this have no solution, one solution or infinite solution
This system of equations has one solution.
To determine the number of solutions for the given system of equations, we can compare the slopes of the two lines. If the slopes are equal, the system has infinite solutions. If the slopes are different, the system has one solution. If the slopes are the same but the y-intercepts are different, the system has no solution.
In the equations y = 3x + 6 and y = -13x - 4, the slopes are 3 and -13, respectively. Since the slopes are different (-13 ≠ 3), the system has one solution.
Therefore, the given system of equations has one solution.
To determine whether the system of equations y = 3x + 6 and y = -13x - 4 has no solution, one solution, or infinite solutions, we need to compare the slopes and y-intercepts of the two equations.
The given equations are in slope-intercept form, y = mx + b, where m represents the slope and b represents the y-intercept.
For the equation y = 3x + 6, the slope is 3 and the y-intercept is 6.
For the equation y = -13x - 4, the slope is -13 and the y-intercept is -4.
Since the slopes of the two equations (-13 and 3) are different, the system of equations represents two lines that are not parallel. This means they will intersect at a single point, resulting in one solution.
Therefore, the system of equations y = 3x + 6 and y = -13x - 4 has one solution.