How many solutions does the system of equations have?
y=4x+4
y=4x-3
y=-6x-2
y+2=-6x
Sorry forgot to put these 2 in as well-
What is the solution of the system?
5x-y =-7
3x-y=-2
What is the solution of the system?
5x+6y=20
9x+11y=32
Ok thx
To find the number of solutions in a system of equations, we need to determine whether the lines represented by the equations intersect, are parallel, or coincide with each other.
For the first system of equations:
y = 4x + 4
y = 4x - 3
Since both equations are in slope-intercept form (y = mx + b), we can compare their slopes (m). In this case, both equations have a slope of 4.
If the slopes are equal, we need to compare the y-intercepts (b). In this case, the y-intercepts are different. One equation has a y-intercept of 4, and the other has a y-intercept of -3.
Since the slopes are equal but the y-intercepts are different, the lines are parallel and will never intersect. Therefore, this system of equations has no solution.
For the second system of equations:
y = -6x - 2
y + 2 = -6x
Both equations are already in slope-intercept form.
Again, we can compare the slopes (m). In this case, both equations also have the same slope of -6.
Next, we compare the y-intercepts (b). In this case, one equation has a y-intercept of -2 and the other equation doesn't have a y-intercept since it has been written in a different form.
Since the slopes are equal and the y-intercepts are different, the lines are parallel and will never intersect. Therefore, this system of equations also has no solution.
In summary, both system of equations have no solutions because the lines represented by the equations are parallel and will never intersect.
For the first one, just subtract the two equations to get
2x = -5
and go from there
For the 2nd set, multiply them a bit to get
45x+54y = 180
45x+55y = 160
Now subtract to get
y = -20
and go from there