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 solve for the point that satisfies both equations y=3x−2y = 3x – 2y=3x−2 and y=−2x+3y = -2x + 3y=−2x+3, we need to find the values of xxx and yyy that make both equations true. We can do this by setting the two equations equal to each other, since both expressions equal yyy.
Given:y=3x−2y = 3x – 2y=3x−2
andy=−2x+3y = -2x + 3y=−2x+3
Set the two expressions for yyy equal:3x−2=−2x+33x – 2 = -2x + 33x−2=−2x+3
Now, let’s solve for xxx:
- Add 2x2x2x to both sides:
3x+2x−2=33x + 2x – 2 = 33x+2x−2=35x−2=35x – 2 = 35x−2=3
- Add 2 to both sides:
5x=55x = 55x=5
- Divide both sides by 5:
x=1x = 1x=1
Now that we have x=1x = 1x=1, substitute it into either of the original equations to find yyy. Let’s use y=3x−2y = 3x – 2y=3x−2:y=3(1)−2=3−2=1y = 3(1) – 2 = 3 – 2 = 1y=3(1)−2=3−2=1
So the point of intersection is (1,1)(1, 1)(1,1).
The correct point that satisfies both equations is (1,1)(1, 1)(1,1). To verify, substitute x=1x = 1x=1 into the second equation y=−2x+3y = -2x + 3y=−2x+3:y=−2(1)+3=−2+3=1y = -2(1) + 3 = -2 + 3 = 1y=−2(1)+3=−2+3=1
Since both equations give the same result, the solution is correct.
Thus, the point that satisfies the system of equations is (1,1)(1, 1)(1,1), and we would select the corresponding option based on the provided options A, B, C, or D, assuming one of them represents (1,1)(1, 1)(1,1).
