Question

The solution to a system of equations is (1, 5). Choose two equations that might make up
the system. Use the graph to prove that your answer is correct.

Answer 1

Answer:

y = 2x + 3 and y = x + 4

Step-by-step explanation:

the first equation:

y = -3x - 6

(5) =-3(1) - 6

5 = 3-6

5≠-3

second equation:

y = 2x + 3

(5) = 2(1) + 3

5 = 2 + 3

5 = 5

third equation:

y = -7x + 1

(5) = -7(1) + 1

5 = -7 + 1

5 ≠ -6

fourth equation:

y = x + 4

(5) = 1 + 4

5 = 5

last equation:

y = -2x - 9

(5) = -2(1) - 9

5 = -2 - 9

5 ≠ -1

Answer 2

Answers:

$y = -2x-9$

$y = x+4$

Step-by-step explanation:

$y = -3x - 6$

This is not the correct answer because it does not go through the point. If you plug in the x and y values you already have into this equation, you would get 5 = -9. This is clearly incorrect.

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$y = 2x+3$

This is the correct answer because it does go through the point. If you plug in the x and y values you already have into this equation, you would get 5 = 5. When you graph this equation using the slope (2) and the y-intercept (3), the line generated would go perfectly through the given point.

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$y = -7x+1$

This is not the correct answer because it does not go through the point. If you plug in the x and y values you already have into this equation, you would get 5 = -6. This is clearly incorrect.

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$y = x+4$

This is the other correct answer because it does go through the point. If you plug in the x and y values you already have into this equation, you would get 5 = 5. When you graph this equation using the slope (1) and the y-intercept (2), the line generated would go perfectly through the given point.

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$y = -2x-9$

This is not the correct answer because it does not go through the point. If you plug in the x and y values you already have into this equation, you would get 5 = -11. This is clearly incorrect.