Question

Use the substitution method to solve the system 2.5x + y = -2,3х + 2y = 0.
(1 point)
O (3, -2)
• no solution
O (-2,3)
• infinite solutions

Answer 1

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

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

**Step 1: Solve one of the equations for one variable.**

Let's solve Equation 1 for \( y \):

\[
y = -2 - 2.5x
\]

**Step 2: Substitute this expression for \( y \) into Equation 2.**

Now substitute \( y \) in Equation 2:

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

Distributing the \( 2 \):

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

Combine like terms:

\[
-2x - 4 = 0
\]

**Step 3: Solve for \( x \)**

Add \( 4 \) to both sides:

\[
-2x = 4
\]

Divide by \(-2\):

\[
x = -2
\]

**Step 4: Substitute \( x \) back to find \( y \)**

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

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

**Step 5: Solution**

So the solution to the system is:

\[
(x, y) = (-2, 3)
\]

Thus, the answer is: \(\boxed{(-2, 3)}\).