Final answer:
To solve the equation 3x−2y=−2, substitute the value of x in the other equation and solve for y. The given equation is a dependent equation with infinitely many solutions.
Step-by-step explanation:
To solve the equation 3x−2y=−2, we can use the method of substitution.
Step 1: Solve one equation for one variable. Let's solve the given equation for x in terms of y:
3x = −2 + 2y
x = (-2 + 2y) / 3
Step 2: Substitute the value of x in the other equation. Let's substitute x = (-2 + 2y) / 3 into the equation 3x−2y = −2:
3((-2 + 2y) / 3) − 2y = −2
-2 + 2y - 2y = −2
-2 = -2
Step 3: Simplify and solve for y:
-2 = -2 (which is true for all values of y)
Since -2 = -2 holds for any value of y, the given equation is dependent. Therefore, it has infinitely many solutions.