Question

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

(−2,3)

left parenthesis negative 2 comma 3 right parenthesis
no solution
no solution
infinite solutions
infinite solutions
(3,−2)

Answer 1

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

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

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

We'll solve the first equation for \(y\):

\[
y = -2 - 2.5x
\]

**Step 2: Substitute this expression for \(y\) into the second equation.**

Substituting \(y\) in the second equation:

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

**Step 3: Simplify and solve for \(x\).**

This simplifies to:

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

Combining like terms gives:

\[
-2x - 4 = 0
\]

Solving for \(x\):

\[
-2x = 4 \implies x = -2
\]

**Step 4: Substitute \(x\) back into the expression for \(y\).**

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

\[
y = -2 - 2.5(-2)
\]

Calculating this gives:

\[
y = -2 + 5 = 3
\]

**Step 5: Write the solution as an ordered pair.**

Thus, the solution to the system of equations is:

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

**Final Answer:**

The solution is \((-2, 3)\).