Question

Solving Simultaneous Equations Using Substitution Quick Check
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Question
Use the substitution method to solve the system 2.5x+y=−2, 3x+2y=0.(1 point)
Responses

infinite solutions
infinite solutions

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

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

no solution
no solution
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Answer 1

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

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

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

Let's solve the first equation for \( y \):

\[
y = -2 - 2.5x
\]

### Step 2: Substitute into the second equation

Now we'll substitute \( y \) into the second equation:

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

Distributing the \( 2 \):

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

### Step 3: Combine like terms

Combine the \( x \) terms:

\[
-2x - 4 = 0
\]

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

Add 4 to both sides:

\[
-2x = 4
\]

Divide by -2:

\[
x = -2
\]

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

Now use this value of \( x \) to find \( y \):

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

Calculating:

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

### Step 6: Write the solution

The solution to the system of equations is:

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

Thus, the correct response from the options given is:

**(−2, 3)**.