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