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 solve the system of equations, we have:

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

We can substitute the expression for \( y \) from Equation 2 into Equation 1.

Substituting \( y = -x + 5 \) into Equation 1:

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

Now, simplify this equation:

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

This simplifies to:

\[
x + 5 = 15
\]

Now, subtract 5 from both sides:

\[
x = 10
\]

Now that we have the value of \( x \), we can substitute it back into Equation 2 to find \( y \):

\[
y = -x + 5
\]

Substituting \( x = 10 \):

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

Thus, the coordinates of the intersection point that solves the system of equations are:

\[
\boxed{(10, -5)}
\]