The point (-4, 6) is a solution to which system?
Responses
{−5x+y=−2−3x+6y=−12
{x+y=2−x+2y=16
{−5x+y=−33x−8y=24
{−4x+y=6−5x−y=21
The system is {−4x+y=6−5x−y=21}.
how any solutions does it have y=5x+7
3y−15x=18
This is a system of two linear equations in two variables:
y = 5x + 7
3y - 15x = 18
We can solve for y in the first equation by subtracting 5x from both sides:
y - 5x = 7
Now we can substitute this expression for y into the second equation:
3(y - 5x) = 18
Expanding and simplifying, we get:
3y - 15x = 18
So the second equation simplifies to the same expression we had before. This means that the two equations are equivalent, and there are infinitely many solutions that satisfy both equations. In fact, any ordered pair (x, y) that satisfies the equation y = 5x + 7 will also satisfy the equation 3y - 15x = 18.
x−2y=6
3x−6y=18 how many solutions
y = 3x + 6
y=−13x−4 how many solutions
To find the solution, we should solve the system of equations:
y = 3x + 6
y = -13x - 4
We can solve for y in the first equation by subtracting 3x from both sides:
y - 3x = 6
Now we can substitute this expression for y into the second equation:
y = -13x - 4
So we get:
-13x - 4 = y = 6 + 3x
Simplifying, we have:
-16x = 2
x = -1/8
Now we can substitute this value of x into either equation to solve for y:
y = 3(-1/8) + 6 = 17/4
So the solution to the system is:
x = -1/8
y = 17/4
Therefore, the system has exactly one solution, which is (-1/8, 17/4).
y=23x−1
y=23x−2 how many solutions
The two equations are both in the form of y = 23x - c, where c is either 1 or 2. This means that both lines have the same slope, 23, but different y-intercepts (-1 for the first equation and -2 for the second equation).
If two lines have different y-intercepts but the same slope, they will be parallel and will never intersect. Therefore, this system of equations has no solution.
The point (-4, 6) is a solution to which system?
Responses
{−5x+y=−33x−8y=24
{−4x+y=6−5x−y=21
{x+y=2−x+2y=16
{−5x+y=−2−3x+6y=−12
The point (-4, 6) is a solution to the system {−4x+y=6, −5x−y=21}.
how many solutions does
y=5x+7
3y−15x=18
To determine how many solutions there are, we can solve the system of equations:
y = 5x + 7
3y - 15x = 18
We can substitute the first equation into the second equation to eliminate y:
3(5x + 7) - 15x = 18
Simplifying:
15x + 21 - 15x = 18
21 = 18
The last equation is not true, which means there is no solution to the system of equations. In other words, the two equations represent two parallel lines that never intersect.
how many solutions does
x−2y=6
3x−6y=18
We can solve the system of equations by using elimination method.
First, we can simplify the second equation by dividing each term by 3:
x - 2y = 6
x - 2y = 6
We can see that the two equations represent the same line, and every point on this line is a solution to the system of equations. Therefore, this system has infinitely many solutions.
how many solutions does
y = 3x + 6
y=−13x−4
In order to find out how many solutions this system has, we can set the two equations equal to each other and solve for x:
3x + 6 = -13x - 4
Adding 13x to both sides gives:
16x + 6 = -4
Subtracting 6 from both sides gives:
16x = -10
Dividing both sides by 16 gives:
x = -10/16 = -5/8
Now we can substitute this value of x into either equation to find the corresponding y-value:
y = 3(-5/8) + 6 = -15/8 + 48/8 = 33/8
So the solution to the system is:
x = -5/8
y = 33/8
Therefore, the system has exactly one solution, which is (-5/8, 33/8).
how many solutions does
y = 3x + 6
y=−1/3x−4
To find out how many solutions this system has, we can set the two equations equal to each other and solve for x:
3x + 6 = -1/3x - 4
Multiplying both sides by 3 gives:
9x + 18 = -x - 12
Adding x and 12 to both sides gives:
10x + 18 = -12
Subtracting 18 from both sides gives:
10x = -30
Dividing both sides by 10 gives:
x = -3
Now we can substitute this value of x into either equation to find the corresponding y-value:
y = 3(-3) + 6 = -3
So the solution to the system is:
x = -3
y = -3
Therefore, the system has exactly one solution, which is (-3, -3).
how many solutions does
y=23x−1
y=23x−2
The two equations are both in the form of y = 23x - c, where c is either 1 or 2. This means that both lines have the same slope, 23, but different y-intercepts (-1 for the first equation and -2 for the second equation).
If two lines have different y-intercepts but the same slope, they will be parallel and will never intersect. Therefore, this system of equations has no solution.