Question

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

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

infinite solutions
infinite solutions

no solution
no solution

Answer 1

To solve this system using the substitution method, we will solve one equation for one variable, and then substitute that expression into the other equation.

First, let's solve the first equation, 2.5x + y = -2, for y.

y = -2 - 2.5x

Now, substitute this expression for y in the second equation, 3x + 2y = 0.

3x + 2(-2 - 2.5x) = 0

3x - 4 - 5x = 0

-2x - 4 = 0

-2x = 4

x = -2

Now, substitute this value of x back into the first equation to solve for y.

2.5(-2) + y = -2

-5 + y = -2

y = -2 + 5

y = 3

Therefore, the solution to the system is (x, y) = (-2, 3).

So, the correct response is: (−2,3)