The point (-4, 6) is a solution to which system?
Responses
{−4x+y=6−5x−y=21
{−5x+y=−2−3x+6y=−12
{x+y=2−x+2y=16
{−5x+y=−33x−8y=24
{−5x+y=−2−3x+6y=−12}
To determine which system of equations the point (-4, 6) is a solution to, we can substitute the given values into each system and check for solutions.
1. {−4x+y=6
−5x−y=21
Substituting x = -4 and y = 6 into the first equation:
−4(-4) + 6 = 6
16 + 6 = 6
22 = 6
This equation is not satisfied, so the point (-4, 6) is not a solution to the first system.
2. {−5x+y=−2
−3x+6y=−12
Substituting x = -4 and y = 6 into the first equation:
−5(-4) + 6 = -2
20 + 6 = -2
26 = -2
This equation is not satisfied, so the point (-4, 6) is not a solution to the second system.
3. {x+y=2
−x+2y=16
Substituting x = -4 and y = 6 into the first equation:
-4 + 6 = 2
2 = 2
This equation is satisfied, so the point (-4, 6) is a solution to the third system.
4. {−5x+y=−33
3x−8y=24
Substituting x = -4 and y = 6 into the first equation:
-5(-4) + 6 = -33
20 + 6 = -33
26 = -33
This equation is not satisfied, so the point (-4, 6) is not a solution to the fourth system.
Therefore, the point (-4, 6) is a solution to the system {x+y=2, −x+2y=16}.
To determine which system the point (-4, 6) is a solution to, we need to substitute the values of x and y into each equation of the system and check if the equations are satisfied.
Let's start by substituting x = -4 and y = 6 into each equation of the systems given:
For the first system:
Equation 1: -4x + y = 6
-4*(-4) + 6 = 16 + 6 = 22, which is not equal to 6.
Equation 2: -5x - y = 21
-5*(-4) - 6 = 20 - 6 = 14, which is not equal to 21.
Since neither equation of the first system is satisfied, (-4, 6) is not a solution to the first system.
For the second system:
Equation 1: -5x + y = -2
-5*(-4) + 6 = 20 + 6 = 26, which is not equal to -2.
Equation 2: -3x + 6y = -12
-3*(-4) + 6*6 = 12 + 36 = 48, which is not equal to -12.
Since neither equation of the second system is satisfied, (-4, 6) is not a solution to the second system.
For the third system:
Equation 1: x + y = 2
-4 + 6 = 2, which is equal to 2.
Equation 2: -x + 2y = 16
-(-4) + 2*6 = 4 + 12 = 16, which is equal to 16.
Both equations of the third system are satisfied, therefore (-4, 6) is a solution to the third system.
For the fourth system:
Equation 1: -5x + y = -33
-5*(-4) + 6 = 20 + 6 = 26, which is not equal to -33.
Equation 2: 3x - 8y = 24
3*(-4) - 8*6 = -12 - 48 = -60, which is not equal to 24.
Since neither equation of the fourth system is satisfied, (-4, 6) is not a solution to the fourth system.
Therefore, (-4, 6) is a solution only to the third system:
{x+y=2, -x+2y=16}.