Bot GPT 3.5
answered
3x + 2y = 2
Subtract 3x from both sides:
2y = -3x + 2
Divide both sides by 2 to solve for y:
y = (-3/2)x + 1
Step-by-Step Bot
answered
Step 1: Solve one of the variables in terms of the other.
Let's solve for x in terms of y:
3x + 2y = 2
Rearranging the equation:
3x = 2 - 2y
Dividing by 3 on both sides:
x = (2 - 2y)/3
Step 2: Substitute the expression found for the variable in the original equation.
Substitute x with (2 - 2y)/3 in the equation 3x + 2y = 2:
3((2 - 2y)/3) + 2y = 2
Simplify:
2 - 2y + 2y = 2
Step 3: Simplify the equation.
The y terms cancel out:
2 = 2
Step 4: Analyze the result.
In this case, the equation simplifies to 2 = 2, which is always true. This means that the original equation is an identity and holds true for all values of x and y.
So, the solution to the equation 3x + 2y = 2 is any pair of values (x, y) that satisfy the equation.
Explain Bot
answered
Let's use the method of substitution to solve this equation. Here's how you can do it:
Step 1: Solve the equation for one variable in terms of the other.
In this case, we can solve the equation for x in terms of y by isolating x.
Starting with the equation: 3x + 2y = 2
Subtract 2y from both sides: 3x = 2 - 2y
Divide both sides by 3: x = (2 - 2y) / 3
Step 2: Substitute the expression you found for x back into the original equation.
Replace x with (2 - 2y) / 3 in the equation: 3((2 - 2y) / 3) + 2y = 2
Simplify: (2 - 2y) + 2y = 2
Combine like terms: 2 - 2y + 2y = 2
The y terms cancel out, leaving you with: 2 = 2
Step 3: Analyze the result
The equation 2 = 2 is always true regardless of the value of y. This means that the given equation 3x + 2y = 2 represents a line in a graph, and any value of x and y that satisfies this equation will lie on the same line.
The solution to this equation is an infinite number of ordered pairs (x, y) that satisfy the equation.
