Question

Find the coordinates of the intersection point that solves the
system of these two linear equations in two variables:
and .
(1 point)
2x + y = 15 y = −x + 5
(−10, 5)
(−5, 10)
(5, −10)
(10, −5)

Answer 1

To find the intersection point of the two linear equations \( 2x + y = 15 \) and \( y = -x + 5 \), we can substitute the expression for \( y \) from the second equation into the first equation.

1. From the second equation, we have:
\[
y = -x + 5
\]

2. Substitute \( y \) in the first equation:
\[
2x + (-x + 5) = 15
\]

3. Simplifying the equation:
\[
2x - x + 5 = 15
\]
\[
x + 5 = 15
\]

4. Now, solve for \( x \):
\[
x = 15 - 5
\]
\[
x = 10
\]

5. Now substitute \( x = 10 \) back into the second equation to find \( y \):
\[
y = -10 + 5
\]
\[
y = -5
\]

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

The correct answer is \( (10, -5) \).