Use the substitution method to solve the system 2.5x+y=−2 , 3x+2y=0 .(1 point) Responses infinite solutions infinite solutions no solution no solution (3,−2) left parenthesis 3 comma negative 2 right parenthesis (−2,3) left parenthesis negative 2 comma 3 right parenthesis
To use the substitution method, we solve one equation for one variable and substitute it into the other equation.
From the first equation, we solve for y in terms of x:
2.5x + y = -2
y = -2.5x - 2
Now we substitute this expression for y into the second equation:
3x + 2(-2.5x - 2) = 0
3x - 5x - 4 = 0
-2x = 4
x = -2
Now we substitute this value of x back into the first equation to solve for y:
2.5(-2) + y = -2
-5 + y = -2
y = 3
Therefore, the solution to the system of equations is (x, y) = (-2, 3).
Thus, the correct response is (−2,3) left parenthesis negative 2 comma 3 right parenthesis.