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Is (−2, 6) a solution to the system of these linear equations: x+2y=10 and 3x+y=0 ? Why?

answers:

Yes, because the graphs intersect at (-2 , 6)

No, because the graphs dont intersect at (-2 , 6)

Yes, because the graphs dont intersect at (-2 , 6)

No, because the graphs intercect at (-2 , 6)

3 answers

To determine if the point (−2, 6) is a solution to the system of equations, we need to substitute \( x = -2 \) and \( y = 6 \) into both equations:

  1. For the first equation \( x + 2y = 10 \): \[ -2 + 2(6) = -2 + 12 = 10 \] This equation is satisfied.

  2. For the second equation \( 3x + y = 0 \): \[ 3(-2) + 6 = -6 + 6 = 0 \] This equation is also satisfied.

Since (−2, 6) satisfies both equations, it is indeed a solution to the system of equations.

Now, regarding the answer choices:

  • Yes, because the graphs intersect at (-2 , 6) is the correct answer.

The other options are incorrect because they don't correctly state the solution status or the nature of the intersection. Thus:

Correct answer: Yes, because the graphs intersect at (-2, 6).

you sure

Yes, I am sure. To confirm that the point \((-2, 6)\) is indeed a solution to the system of equations, let's summarize the checks we performed:

  1. For the first equation \(x + 2y = 10\):

    • Substituting \((-2, 6)\): \[ -2 + 2(6) = -2 + 12 = 10 \quad \text{(satisfied)} \]

  2. For the second equation \(3x + y = 0\):

    • Substituting \((-2, 6)\): \[ 3(-2) + 6 = -6 + 6 = 0 \quad \text{(satisfied)} \]

Since both equations are satisfied, \((-2, 6)\) is indeed a solution to the system.

Regarding the answer options you provided, the correct choice is:

Yes, because the graphs intersect at (-2, 6).

This is the correct answer because \((-2, 6)\) is a point of intersection for the graphs of the two equations, confirming it as a solution. If you have any further questions or need clarification, feel free to ask!