Question

Solve using system of equations and answer with the x coordinate


-2x+y=5
-5x+y=-4

Answer 1

To solve the system of equations

\[
-2x + y = 5 \quad (1)
\]
\[
-5x + y = -4 \quad (2)
\]

we can use the substitution or elimination method. Here, I'll use the elimination method.

1. Start by isolating \( y \) in both equations:
From equation (1):
\[
y = 2x + 5 \quad (3)
\]

From equation (2):
\[
y = 5x - 4 \quad (4)
\]

2. Set the expressions for \( y \) in equations (3) and (4) equal to each other:
\[
2x + 5 = 5x - 4
\]

3. Now, solve for \( x \):
\[
2x + 5 + 4 = 5x
\]
\[
9 = 5x - 2x
\]
\[
9 = 3x
\]
\[
x = 3
\]

Thus, the x-coordinate is \( \boxed{3} \).