Question

How many solution(s) does the system of equations have?
5x +y=-18
10x - 2y = 36 (1 point)
• none
• one
• two
• infinite

Answer 1

Only the answer

Answer 2

To determine the number of solutions for the given system of equations, we can analyze the equations:

1. \( 5x + y = -18 \)
2. \( 10x - 2y = 36 \)

We can simplify the second equation. Notice that if we divide the entire equation by 2, we have:

\[
5x - y = 18
\]

Now we can rewrite the system of equations:

1. \( 5x + y = -18 \) (Equation 1)
2. \( 5x - y = 18 \) (Equation 2)

Next, we can solve for \( y \) in terms of \( x \) from both equations:

From Equation 1:
\[
y = -18 - 5x
\]

From Equation 2:
\[
-y = 18 - 5x \quad \Rightarrow \quad y = 5x - 18
\]

Now, we have two expressions for \( y \):
1. \( y = -18 - 5x \)
2. \( y = 5x - 18 \)

Setting these equal to each other to find \( x \):
\[
-18 - 5x = 5x - 18
\]

Adding \( 5x \) to both sides:
\[
-18 = 10x - 18
\]

Adding \( 18 \) to both sides:
\[
0 = 10x
\]

This gives us:
\[
x = 0
\]

Now, substitute \( x = 0 \) back into either equation to solve for \( y \). Using Equation 1:
\[
y = -18 - 5(0) = -18
\]

So, we find a single solution:
\[
(x, y) = (0, -18)
\]

Therefore, the system of equations has **one** solution.

Answer 3

One.