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

Question

2
x
+
y
=
15
and y=−x+5
y
=
−
x
+
5
.

(1 point)
Responses

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

(−10, 5)
(
−
10
,

5
)
left parenthesis negative 10 comma 5 right parenthesis

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

(−5, 10)

Answer 1

To find the coordinates of the intersection point of the two equations:

1. First equation: \( 2x + y = 15 \)
2. Second equation: \( y = -x + 5 \)

We'll substitute the expression from the second equation into the first equation.

Starting with the first equation:

\[ 2x + y = 15 \]

Substituting \( y = -x + 5 \):

\[ 2x + (-x + 5) = 15 \] \[ 2x - x + 5 = 15 \] \[ x + 5 = 15 \] \[ x = 15 - 5 \] \[ x = 10 \]

Now that we have \( x = 10 \), we can substitute this value back into the second equation to find \( y \):

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

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

The correct response is:

\((10, -5)\)