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Find the coordinates of the intersection point that solves the system of these two linear equations in two variables: 2x+y=15 and y=−x+5.

(1 point)
Responses

(10,−5)
left parenthesis 10 comma negative 5 right parenthesis

(5,−10)
left parenthesis 5 comma negative 10 right parenthesis

(−10, 5)
left parenthesis negative 10 comma 5 right parenthesis

(−5, 10)

1 answer

To find the coordinates of the intersection point that solves the system of the two linear equations \(2x + y = 15\) and \(y = -x + 5\), we can use substitution.

  1. We can substitute the expression for \(y\) from the second equation into the first equation.

Substituting \(y = -x + 5\) into \(2x + y = 15\):

\[ 2x + (-x + 5) = 15 \]

  1. Simplify the equation:

\[ 2x - x + 5 = 15 \]

  1. Combine like terms:

\[ x + 5 = 15 \]

  1. Solve for \(x\):

\[ x = 15 - 5 = 10 \]

  1. Now, substitute \(x = 10\) back into the second equation to find \(y\):

\[ y = -x + 5 = -10 + 5 = -5 \]

Thus, the intersection point is \((10, -5)\).

The correct response is:

(10, −5)