y = 3x + 6
y = -13x - 4
does this have no solution, one solution or infinite solution
what makes it one solution please explain
To determine the number of solutions for this system of equations, we need to compare their slopes.
In the first equation, y = 3x + 6, the slope is 3.
In the second equation, y = -13x - 4, the slope is -13.
Since the slopes are different, the lines represented by these equations will intersect at a single point, meaning there is only one solution. This occurs when the lines have different slopes and are not parallel to each other.
To determine the number of solutions for the given system of equations, we can compare the slopes (coefficients of x) of the two equations.
The given equations are:
1) y = 3x + 6
2) y = -13x - 4
Since the slopes of the two equations are different (3 and -13), the lines represented by these equations will not be parallel and will intersect at a single point.
Hence, the system of equations has one solution.
To determine if the system of equations has no solution, one solution, or infinite solutions, we need to find the intersection point (if it exists) of the lines represented by the equations.
In this case, we have the equations:
1) y = 3x + 6
2) y = -13x - 4
To find the intersection point, we can set the two equations equal to each other and solve for x:
3x + 6 = -13x - 4
Combining like terms:
3x + 13x = -4 - 6
16x = -10
Divide both sides by 16:
x = -10/16
x = -5/8
Now, substitute this value of x back into either equation to find the value of y.
Let's use equation 1:
y = 3(-5/8) + 6
y = -15/8 + 48/8
y = 33/8
Therefore, the intersection point is (-5/8, 33/8).
Since we have determined a single point of intersection, this system of equations has one solution.