Question

Use the substitution method to solve the system 2.5x+y=−2, 3x+2y=0.(1 point)%0D%0AResponses%0D%0A%0D%0Ainfinite solutions%0D%0Ainfinite solutions%0D%0A%0D%0A(−2,3)%0D%0Aleft parenthesis negative 2 comma 3 right parenthesis%0D%0A%0D%0A(3,−2)%0D%0Aleft parenthesis 3 comma negative 2 right parenthesis%0D%0A%0D%0Ano solution

Answer 1

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

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

### Step 1: Solve Equation 1 for \( y \)

From Equation 1, we can express \( y \) in terms of \( x \):

\[
y = -2 - 2.5x
\]

### Step 2: Substitute \( y \) into Equation 2

Now, we substitute this expression for \( y \) into Equation 2:

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

### Step 3: Simplify and solve for \( x \)

Expanding the equation:

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

Combine like terms:

\[
-2x - 4 = 0
\]

Adding 4 to both sides:

\[
-2x = 4
\]

Dividing by -2 gives:

\[
x = -2
\]

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

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

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

### Final solution

Thus, the solution to the system of equations is:

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

**Answer: \( (-2, 3) \)**