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 two equations:

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

### Step 1: Solve one of the equations for one variable
Let's solve the first equation for \( y \).

\[
y = -2 - 2.5x
\]

### Step 2: Substitute this expression into the other equation
Now we substitute this expression for \( y \) into the second equation.

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

### Step 3: Distribute and simplify
\[
3x - 4 - 5x = 0
\]

Combining like terms:
\[
-2x - 4 = 0
\]

### Step 4: Solve for \( x \)
\[
-2x = 4 \implies x = -2
\]

### Step 5: Substitute back to find \( y \)
Now that we have \( x = -2 \), we substitute it back into the equation for \( y \):

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

### Step 6: Write the solution
The solution to the system is \( (x, y) = (-2, 3) \).

### Conclusion
The correct response is:
\[
\boxed{(-2, 3)}
\]