Question

Use the substitution method to solve the system 2.5x+y=−2
, 3x+2y=0
.(1 point)
Responses

infinite solutions
infinite solutions

(3,−2)
left parenthesis 3 comma negative 2 right parenthesis

(−2,3)
left parenthesis negative 2 comma 3 right parenthesis

no solution

Answer 1

To solve the system of equations using the substitution method, we start with the given equations:

1. \( 2.5x + y = -2 \) (Equation 1)
2. \( 3x + 2y = 0 \) (Equation 2)

### Step 1: Solve one equation for one variable

We can solve Equation 1 for \( y \):

\[
y = -2 - 2.5x
\]

### Step 2: Substitute into the other equation

Now we'll substitute \( y \) into Equation 2:

\[
3x + 2(-2 - 2.5x) = 0
\]

Expanding this gives:

\[
3x - 4 - 5x = 0
\]

### Step 3: Combine like terms

Combine the \( x \) terms:

\[
3x - 5x - 4 = 0
\]
\[
-2x - 4 = 0
\]

### Step 4: Solve for \( x \)

Adding 4 to both sides:

\[
-2x = 4
\]

Now divide by -2:

\[
x = -2
\]

### Step 5: Substitute back to find \( y \)

Now substitute \( x = -2 \) back into the equation we found for \( y \):

\[
y = -2 - 2.5(-2)
\]
\[
y = -2 + 5 = 3
\]

Thus, we have \( x = -2 \) and \( y = 3 \).

### Final Solution

The solution to the system is:

\[
(-2, 3)
\]

Thus, the correct answer is:

**(−2, 3)** (left parenthesis negative 2 comma 3 right parenthesis).