Question

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

O infinite solutions
O (-2,3)
O no solution
O (3,-2)

Answer 1

[AI-generated answer — Bot GPT 3.5]

To solve the system of equations using the substitution method, we can solve one equation for one variable and substitute it into the other equation.

Let's start with the first equation:

2.5x + y = -2

Let's solve this equation for y:

y = -2 - 2.5x

Now we can substitute this value of y into the second equation:

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

Simplify the equation:

3x - 4 - 5x = 0

Combine like terms:

-2x - 4 = 0

Add 4 to both sides:

-2x = 4

Divide by -2:

x = -2

Now that we have the value of x, we can substitute it back into the first equation to find y:

2.5(-2) + y = -2

-5 + y = -2

Add 5 to both sides:

y = 3

So the solution to the system of equations is (x, y) = (-2, 3).

Therefore, the correct answer is:
O (-2,3)