use the subsitution method to solve the system 2.5x+y=-2, 3x+2y=0

Question

A: no solution
B:(-2,3)
C:(3, 2)
D:infinite solutions

Answer 1

To use the substitution method, we can start by solving the first equation for y:

2.5x + y = -2
y = -2.5x - 2

Now we can substitute this expression for y into the second equation:

3x + 2(-2.5x - 2) = 0
3x - 5x - 4 = 0
-2x - 4 = 0
-2x = 4
x = -2

Now that we have found the value of x, we can substitute it 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 of equations is (-2, 3), which corresponds to answer choice B.