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 .

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. Start with the equations:
\[
2x + y = 15 \quad \text{(1)}
\]
\[
y = -x + 5 \quad \text{(2)}
\]

2. Substitute equation (2) into equation (1):
\[
2x + (-x + 5) = 15
\]

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

4. Solve for \( x \):
\[
x = 15 - 5 = 10
\]

5. Now, substitute \( x = 10 \) back into equation (2) to find \( y \):
\[
y = -10 + 5 = -5
\]

6. Therefore, the coordinates of the intersection point are:
\[
(10, -5)
\]

So, the solution to the system of equations is:
\[
\boxed{(10, -5)}
\]