1.How many solutions does the system of equations have?
y=6x+2
y=6x+4
a. one
b. two
c. infinite
d. none
2. How many solutions does the system of equations have?
y=1/2x-3
x-2y=6
a. one
b. two
c. infinitely many
d. none
3. How many solutions does the system of equations have?
y-6=-3
y-6x=-6
a. one
b. two
c. none
d. infinitely many
I just do not get this at all it would be nice if you could show me how you get this.
get all the equations into slope-intercept form (y = mx + b)
1. the slopes are the same but the intercepts are different
... the lines are parallel
... they never intersect so no solution
2. the slopes are the same and so are the intercepts
... the lines lie on top of each other
... an infinite number of solutions
3. the slopes are different
... the lines intersect
... one solution
Y=-2x+2
Y=-2x-2
Y=3x-2
Y=2(x-1)
1. How many solutions does the system of equations have?
y=6x+2
y=6x+4
Since the slopes (coefficients of x) for both equations are equal, but the y-intercepts (constants) are different, the lines are parallel. Parallel lines never intersect, so the system of equations has no solution. Choice d. none.
2. How many solutions does the system of equations have?
y=1/2x-3
x-2y=6
To determine the number of solutions, we need to compare the slopes of the two equations. The equation y=1/2x-3 has a slope of 1/2, while the equation x-2y=6 can be rewritten as y=1/2x-3. Thus, both equations represent the same line, and they intersect at every point on that line. Therefore, the system of equations has infinitely many solutions. Choice c. infinitely many.
3. How many solutions does the system of equations have?
y-6=-3
y-6x=-6
To determine the number of solutions, let's simplify the equations:
y-6=-3 --> y=3
y-6x=-6 --> y=6x-6
Since the equation y=3 is different from the equation y=6x-6, the lines represented by these equations are parallel. Therefore, the system of equations has no solution. Choice c. none.
I hope that helps clarify the solutions for you! If you have any more questions, feel free to ask!
To determine the number of solutions for each system of equations, we can use a simple method of comparison. By comparing the coefficients and constants in the equations, we can identify the relationship between the lines they represent in the coordinate plane.
1. The given system of equations is:
y = 6x + 2
y = 6x + 4
We notice that both equations have the same slope (6x) but different y-intercepts (2 and 4). Since the lines have the same slope but different y-intercepts, they are parallel to each other.
Parallel lines never intersect, so this system of equations has no solutions.
Answer: d. none
2. The given system of equations is:
y = 1/2x - 3
x - 2y = 6
These two equations have different slopes (1/2 and -2) and different y-intercepts (-3 and 0). We can solve this system of equations by substitution or elimination methods to find a unique solution.
Let's solve it using elimination:
Multiply the first equation by 2 to simplify the coefficient of y:
2y = x - 6
Now, our system of equations is:
2y = x - 6
x - 2y = 6
Adding these two equations eliminates the variable y:
0x + 0 = 12
This equation simplifies to 0 = 12, which is not true. When an equation leads to a false statement, there are no solutions.
Answer: d. none
3. The given system of equations is:
y - 6 = -3
y - 6x = -6
Let's solve it using the elimination method:
Subtract the first equation from the second equation:
(y - 6x) - (y - 6) = -6 - (-3)
y - 6x - y + 6 = -6 + 3
-6x + 6 = -3
Simplify:
-6x = -3 - 6
-6x = -9
x = -9 / -6
x = 3/2
Substitute the value of x back into one of the equations to find y:
y - 6 = -3
y = -3 + 6
y = 3
We found a unique solution for both x and y.
Answer: a. one
By following the steps described above and comparing the equations, we can determine the number of solutions for each system.
Y=6x-10
Y=2(3x-5)
Y=6x-10
Y=2(3x-5)
Tell if the system has one,none,or infinite solutions