Use the substitution method to solve the system 2.5x+y=−2 , 3x+2y=0 .(1 point) Responses no solution no solution (3,−2) left parenthesis 3 comma negative 2 right parenthesis infinite solutions infinite solutions (−2,3)
To use the substitution method, we can start by solving one of the equations for one variable and substituting it into the other equation.
From the first equation, we can solve for y by subtracting 2.5x from both sides:
y = -2 - 2.5x
Next, we can substitute this expression for y in the second equation:
3x + 2(-2 - 2.5x) = 0
Simplifying the equation:
3x - 4 - 5x = 0
-2x - 4 = 0
-2x = 4
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
y = 3
Therefore, the solution to the system is (x, y) = (-2, 3).