Question

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 negative 10 comma 5 right parenthesis

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

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

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

Answer 1

To find the intersection point of the two linear equations, we can substitute one equation into the other since the second equation is already solved for \(y\).

We have the equations:

1. \(2x + y = 15\)
2. \(y = -x + 5\)

Substituting \(y\) from equation 2 into equation 1:

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

This simplifies to:

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

Combining like terms gives:

\[
x + 5 = 15
\]

Subtracting 5 from both sides:

\[
x = 10
\]

Now that we have \(x\), we can substitute it back into equation 2 to find \(y\):

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

Thus, the coordinates of the intersection point are:

\((10, -5)\).

The correct response is:

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