y=3x+6
y=-13x-4 is this one solution or no solution or infinite solutions
To find out if the system of equations has a solution, no solution, or infinite solutions, we can compare the slopes of the two lines.
The equation y = 3x + 6 has a slope of 3.
The equation y = -13x - 4 has a slope of -13.
Since the slopes are not equal, the two lines will intersect at a single point, resulting in one solution.
To determine whether the given system of equations has one solution, no solution, or infinite solutions, we need to compare the slopes and y-intercepts of the equations.
For the first equation, y = 3x + 6, the slope is 3 and the y-intercept is 6.
For the second equation, y = -13x - 4, the slope is -13 and the y-intercept is -4.
Since the slopes of the two equations are different (-13 ≠ 3), the lines represented by these equations will intersect at some point. Therefore, the system of equations has one solution.
To determine whether this system of equations has one solution, no solution, or infinitely many solutions, we can compare the slopes (coefficients of x) and y-intercepts (constant terms).
Given the system:
1) y = 3x + 6
2) y = -13x - 4
For one solution to exist:
1) The slopes of the lines must be different.
2) The y-intercepts must also be different.
Comparing the slopes:
The slope of the first equation (1) is 3, while the slope of the second equation (2) is -13. Since the slopes are different, one solution is possible.
Comparing the y-intercepts:
The y-intercept of the first equation (1) is 6, while the y-intercept of the second equation (2) is -4. Since the y-intercepts are different, one solution is possible.
Therefore, based on the comparison of slopes and y-intercepts, this system of equations has one solution.