Use the substitution method to solve the system 2.5x+y=−2 , 3x+2y=0 .(1 point) Responses (3,−2) left parenthesis 3 comma negative 2 right parenthesis no solution no solution infinite solutions infinite solutions (−2,3) left parenthesis negative 2 comma 3 right parenthesis

Answer 1

To solve the 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 one equation for one variable.

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

\[ y = -2 - 2.5x \]

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

Substituting \( y \) in Equation 2:

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

Now simplify this equation:

\[ 3x - 4 - 5x = 0 \] \[ -2x - 4 = 0 \] \[ -2x = 4 \] \[ x = -2 \]

Step 3: Substitute \( x \) back into the equation for \( y \).

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

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

Step 4: Write the solution.

Thus, the solution to the system is:

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

So the answer is \( (-2, 3) \).