Question

The point (5, -3) is a solution to which system of equations?(1 point)

Responses

a y=x+2
y=x+5

b y=x-8
2x+y=7

c y= - 1/2 x+6
y=3x-1

d y=2/3x+6
3y+6x-18=0

Answer 1

[AI-generated answer — Bot GPT 3.5]

To determine which system of equations the point (5, -3) is a solution to, we substitute the x-coordinate (=5) and the y-coordinate (=-3) into each of the given equations and check if they are true.

(a) For y = x + 2:
-3 ≠ 5 + 2,
This equation is not true for the given point (5, -3).

(b) For y = x - 8 and 2x + y = 7:
-3 = 5 - 8,
This equation is true for the given point (5, -3).

(c) For y = -1/2x + 6 and y = 3x - 1:
-3 = -1/2(5) + 6
-3 = -5/2 + 6
-3 = -5/2 + 12/2
-3 = 7/2,
This equation is not true for the given point (5, -3).

(d) For y = 2/3x + 6 and 3y + 6x - 18 = 0:
-3 = 2/3(5) + 6
-3 = 10/3 + 6
-3 = 10/3 + 18/3
-3 = 28/3,
This equation is not true for the given point (5, -3).

Therefore, the point (5, -3) is a solution to the system of equations in option (b):

y = x - 8
2x + y = 7

Answer 2

[AI-generated answer — Step-by-Step Bot]

To determine which system of equations the point (5, -3) is a solution to, we need to substitute the x and y values of the point into each equation of the systems and see if it satisfies both equations.

a) y = x + 2
(-3) = (5) + 2
-3 does not equal 7, so the point (5, -3) is not a solution to this system.

b) y = x - 8
(-3) = (5) - 8
-3 does not equal -3, so the point (5, -3) is not a solution to this system.

c) y = -1/2 x + 6
(-3) = -1/2 (5) + 6
-3 does equal -1/2 + 6, so the point (5, -3) is a solution to this equation.

d) y = 2/3x + 6
(-3) = 2/3(5) + 6
-3 does equal 10/3 + 6, so the point (5, -3) is not a solution to this equation.

Thus, the point (5, -3) is a solution to the system of equations:
c) y = -1/2 x + 6
y = 3x - 1

Answer 3

[AI-generated answer — Explain Bot]

To determine which system of equations the point (5, -3) is a solution to, we can substitute the values of x and y from the point (5, -3) into each equation of the given systems and check for solutions. Here, we will substitute x = 5 and y = -3 into each equation and see which system gives us true statements.

a) Substituting x = 5 and y = -3 into the first equation y = x + 2:
-3 = 5 + 2
-3 = 7 (which is not true)

Substituting x = 5 and y = -3 into the second equation y = x + 5:
-3 = 5 + 5
-3 = 10 (which is not true)

Since neither equation in system a) is true when x = 5 and y = -3, system a) is NOT the solution.

b) Substituting x = 5 and y = -3 into the first equation y = x - 8:
-3 = 5 - 8
-3 = -3 (which is true)

Substituting x = 5 and y = -3 into the second equation 2x + y = 7:
2(5) + (-3) = 7
10 - 3 = 7
7 = 7 (which is true)

Both equations in system b) are true when x = 5 and y = -3, so system b) IS the solution.

c) Substituting x = 5 and y = -3 into the first equation y = -1/2x + 6:
-3 = -1/2(5) + 6
-3 = -2.5 + 6
-3 = 3.5 (which is not true)

Substituting x = 5 and y = -3 into the second equation y = 3x - 1:
-3 = 3(5) - 1
-3 = 15 - 1
-3 = 14 (which is not true)

Neither equation in system c) is true when x = 5 and y = -3, so system c) is NOT the solution.

d) Substituting x = 5 and y = -3 into the first equation y = 2/3x + 6:
-3 = 2/3(5) + 6
-3 = 10/3 + 6
-3 = 28/3 (which is not true)

Substituting x = 5 and y = -3 into the second equation 3y + 6x - 18 = 0:
3(-3) + 6(5) - 18 = 0
-9 + 30 - 18 = 0
3 = 0 (which is not true)

Neither equation in system d) is true when x = 5 and y = -3, so system d) is NOT the solution.

Therefore, the answer is b) y = x - 8 and 2x + y = 7