Which point satisfies the system of equations y = 3x – 2 and y = -2x + 3? A. A B. B C. C D. D
The Correct Answer and Explanation is:
To find the point that satisfies both equations, we need to solve the system of equations:
- y=3x−2y = 3x – 2y=3x−2
- y=−2x+3y = -2x + 3y=−2x+3
Step 1: Set the equations equal to each other
Since both equations are equal to yyy, we can set the right-hand sides equal to each other:3x−2=−2x+33x – 2 = -2x + 33x−2=−2x+3
Step 2: Solve for xxx
First, add 2x2x2x to both sides to move all terms with xxx to one side:3x+2x−2=33x + 2x – 2 = 33x+2x−2=3
Simplify:5x−2=35x – 2 = 35x−2=3
Next, add 2 to both sides to isolate the term with xxx:5x=55x = 55x=5
Now, divide both sides by 5:x=1x = 1x=1
Step 3: Solve for yyy
Now that we have x=1x = 1x=1, substitute this value into either of the original equations. Let’s use the first equation:y=3x−2y = 3x – 2y=3x−2
Substitute x=1x = 1x=1:y=3(1)−2=3−2=1y = 3(1) – 2 = 3 – 2 = 1y=3(1)−2=3−2=1
So, the point that satisfies both equations is (1,1)(1, 1)(1,1).
Conclusion:
The point (1,1)(1, 1)(1,1) is the solution to the system of equations. Therefore, the correct answer is the point that corresponds to this value on the given options.
