Use the substitution method to solve the system 2.5x+y=−2 , 3x+2y=0 .(1 point)
Responses
(3,−2)
(−2,3)
infinite solutions
no solution
To solve the system of equations using the substitution method, we first solve one equation for one variable and substitute it into the other equation.
From the first equation, we solve for y:
2.5x + y = -2
y = -2 - 2.5x
Now, we substitute this expression for y into the second equation:
3x + 2(-2 - 2.5x) = 0
3x - 4 - 5x = 0
-2x - 4 = 0
-2x = 4
x = -2
We now substitute this value of x 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 (x, y) = (-2, 3).
The correct response is (−2,3).