The point (5, -3) is a solution to which system of equations?
A. y=c+2
y=x+5
B. y=-1/2x +6
y=3x-1
C. y=2/3x+6
3y+6x-18=0
D. y=x-8
2x+y=7
The point (5, -3) is a solution to the system of equations in option D.
By substituting x = 5 and y = -3 into the equations:
For the first equation, y = x - 8, we have:
-3 = 5 - 8
-3 = -3
For the second equation, 2x + y = 7, we have:
2(5) + (-3) = 7
10 - 3 = 7
7 = 7
Since both equations result in true statements, the point (5, -3) is a solution to the system of equations in option D.
To determine which system of equations the point (5, -3) is a solution to, we need to substitute the values of x and y into each equation in each system of equations and check if they are satisfied. Let's go through each option one by one:
A. y = c + 2
y = x + 5
Let's substitute x = 5 and y = -3 into these equations:
-3 = c + 2 --> c = -5 (First equation)
-3 = 5 + 5 --> -3 = 10 (Second equation)
Since -3 does not equal 10, the point (5, -3) is not a solution to this system.
B. y = -1/2x + 6
y = 3x - 1
Substituting x = 5 and y = -3 into these equations:
-3 = -1/2 * 5 + 6 --> -3 = -5/2 + 6 --> -3 = 7/2 (First equation)
-3 = 3 * 5 - 1 --> -3 = 15 - 1 --> -3 = 14 (Second equation)
Since -3 does not equal 7/2 or 14, the point (5, -3) is not a solution to this system.
C. y = 2/3x + 6
3y + 6x - 18 = 0
Substituting x = 5 and y = -3 into these equations:
-3 = 2/3 * 5 + 6 --> -3 = 10/3 + 6 --> -3 = 28/3 (First equation)
3(-3) + 6(5) - 18 = 0 --> -9 + 30 - 18 = 3 --> 3 = 3 (Second equation)
Since -3 does not equal 28/3, the point (5, -3) is not a solution to this system.
D. y = x - 8
2x + y = 7
Substituting x = 5 and y = -3 into these equations:
-3 = 5 - 8 (First equation)
2(5) + (-3) = 7 --> 10 - 3 = 7 --> 7 = 7 (Second equation)
The point (5, -3) satisfies both equations, so it is a solution to this system.
Therefore, the point (5, -3) is a solution to the system of equations:
y = x - 8
2x + y = 7
The answer is D.
To determine which system of equations the point (5, -3) is a solution to, we need to substitute the coordinates into each equation and check if they satisfy the equation.
A. Substituting (5, -3) into the equations:
For the first equation, y = c + 2, we don't have enough information to determine if (5, -3) satisfies the equation.
For the second equation, y = x + 5:
-3 = 5 + 5
-3 = 10 (not true for the given point)
B. Substituting (5, -3) into the equations:
For the first equation, y = (-1/2)x + 6:
-3 = (-1/2)(5) + 6
-3 = -5/2 + 6
-3 = -5/2 + 12/2
-3 = 7/2 (not true for the given point)
For the second equation, y = 3x - 1, we don't have enough information to determine if (5, -3) satisfies the equation.
C. Substituting (5, -3) into the equations:
For the first equation, y = (2/3)x + 6:
-3 = (2/3)(5) + 6
-3 = 10/3 + 18/3
-3 = 28/3 (not true for the given point)
For the second equation, 3y + 6x - 18 = 0:
3(-3) + 6(5) - 18 = 0
-9 + 30 - 18 = 0
3 = 0 (not true for the given point)
D. Substituting (5, -3) into the equations:
For the first equation, y = x - 8:
-3 = 5 - 8
-3 = -3 (true for the given point)
For the second equation, 2x + y = 7:
2(5) + (-3) = 7
10 - 3 = 7
7 = 7 (true for the given point)
From the calculations, we can see that the point (5, -3) is a solution to system D:
y = x - 8
2x + y = 7