Use the substitution method to solve the system 2.5x+y=−2 , 3x+2y=0 .(1 point)Responses(−2,3)left parenthesis negative 2 comma 3 right parenthesisno solutionno solutioninfinite solutionsinfinite solutions(3,−2)
To solve the system of equations using the substitution method, we start by solving one of the equations for one variable and then substituting it into the other equation.
From the first equation, we can solve for y:
2.5x + y = -2
Subtract 2.5x from both sides:
y = -2.5x - 2
Now, we substitute this value of y into the second equation:
3x + 2(-2.5x - 2) = 0
Distribute:
3x - 5x - 4 = 0
Combine like terms:
-2x - 4 = 0
Add 4 to both sides:
-2x = 4
Divide by -2:
x = -2
Now that we have x, we can substitute it back into the first equation to solve for y:
2.5(-2) + y = -2
-5 + y = -2
Add 5 to both sides:
y = 3
Therefore, the solution to the system of equations is (x, y) = (-2, 3).