−4x+6y=38
x−5y=−20
(35, −3)
left parenthesis 35 comma negative 3 right parenthesis
(5, 3)
left parenthesis 5 comma 3 right parenthesis
(−5, 3)
left parenthesis negative 5 comma 3 right parenthesis
(−35, −3)
left parenthesis negative 35 comma negative 3 right parenthesis
To check if the given points are solutions to the system of equations, substitute the values of x and y into each equation and see if the equation is true.
Let's check each point one by one:
1. For the point (35, -3):
-4x + 6y = 38
Substitute x = 35 and y = -3:
-4(35) + 6(-3) = 38
-140 -18 = 38
-158 = 38
The equation is not true, so (35, -3) is not a solution.
2. For the point (5, 3):
-4x + 6y = 38
Substitute x = 5 and y = 3:
-4(5) + 6(3) = 38
-20 + 18 = 38
-2 = 38
The equation is not true, so (5, 3) is not a solution.
3. For the point (-5, 3):
-4x + 6y = 38
Substitute x = -5 and y = 3:
-4(-5) + 6(3) = 38
20 + 18 = 38
38 = 38
The equation is true, so (-5, 3) is a solution.
4. For the point (-35, -3):
-4x + 6y = 38
Substitute x = -35 and y = -3:
-4(-35) + 6(-3) = 38
140 - 18 = 38
122 = 38
The equation is not true, so (-35, -3) is not a solution.
Therefore, the only solution to the system of equations is (-5, 3).
To find out which of the given points satisfy the system of equations, let's substitute the values of x and y into the two equations and see if they are true.
1. For the point (35, -3):
Substituting x = 35 and y = -3 into the equations:
-4(35) + 6(-3) = 38 Simplifying this equation gives: -140 - 18 = 38, which is false.
35 - 5(-3) = -20 Simplifying this equation gives: 35 + 15 = -20, which is false.
Since both equations are false, the point (35, -3) does not satisfy the system of equations.
2. For the point (5, 3):
Substituting x = 5 and y = 3 into the equations:
-4(5) + 6(3) = 38 Simplifying this equation gives: -20 + 18 = 38, which is false.
5 - 5(3) = -20 Simplifying this equation gives: 5 - 15 = -20, which is also false.
Again, both equations are false, so the point (5, 3) does not satisfy the system of equations.
3. For the point (-5, 3):
Substituting x = -5 and y = 3 into the equations:
-4(-5) + 6(3) = 38 Simplifying this equation gives: 20 + 18 = 38, which is true.
-5 - 5(3) = -20 Simplifying this equation gives: -5 - 15 = -20, which is also true.
Both equations are true, so the point (-5, 3) satisfies the system of equations.
4. For the point (-35, -3):
Substituting x = -35 and y = -3 into the equations:
-4(-35) + 6(-3) = 38 Simplifying this equation gives: 140 - 18 = 38, which is false.
-35 - 5(-3) = -20 Simplifying this equation gives: -35 + 15 = -20, which is also false.
Both equations are false, so the point (-35, -3) does not satisfy the system of equations.
Therefore, out of the given points, only the point (-5, 3) satisfies the system of equations.