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Is (-2, 6) a solution to the system of these linear equations: x + 2y = 10 and 3x+y=0? Why? (1 point)

No, because the graphs intersect at (-2, 6).
No, because the graphs don't intersect at (-2, 6).
O Yes, because the graphs don't intersect at (-2, 6).
O Yes, because the graphs intersect at (-2,6)

3 answers

To determine if the point (-2, 6) is a solution to the system of equations given by \( x + 2y = 10 \) and \( 3x + y = 0 \), we can plug in the values of \( x \) and \( y \) 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.

The correct interpretation regarding the intersection of the graphs of these equations is: Yes, because the graphs intersect at (-2, 6).

Estimate the solution to the system of these linear equations based on the graph. y=5x+10 y=−2x+3 (1 point) Responses (−1,−5) left parenthesis negative 1 comma negative 5 right parenthesis (5,−1) left parenthesis 5 comma negative 1 right parenthesis (1, 5) left parenthesis 1 comma 5 right parenthesis (−1, 5)

To estimate the solution to the system of equations given by \( y = 5x + 10 \) and \( y = -2x + 3 \), we can set the two equations equal to each other to find the point of intersection:

  1. Set the equations equal: \[ 5x + 10 = -2x + 3 \]

  2. Solve for \( x \): \[ 5x + 2x = 3 - 10 \] \[ 7x = -7 \] \[ x = -1 \]

  3. Substitute \( x = -1 \) into one of the original equations to find \( y \). We can use either one; we'll use the second equation: \[ y = -2(-1) + 3 = 2 + 3 = 5 \]

The solution to the system of equations is \( (-1, 5) \).

Thus, based on the options you provided, the correct response is: (−1, 5).