Find 3 solutions (ordered pairs) for the equation 3x – 2y = 12
The Correct Answer and Explanation is:
To find the solutions for the equation 3x−2y=123x – 2y = 123x−2y=12, we will solve for ordered pairs (x,y)(x, y)(x,y) by choosing different values for xxx and solving for yyy.
Step-by-Step Process:
- Rewrite the equation for yyy: 3x−2y=12⇒−2y=12−3x⇒y=3x−1223x – 2y = 12 \quad \Rightarrow \quad -2y = 12 – 3x \quad \Rightarrow \quad y = \frac{3x – 12}{2}3x−2y=12⇒−2y=12−3x⇒y=23x−12 This equation tells us that for each value of xxx, we can substitute it in and solve for yyy.
Solution 1:
Let x=0x = 0x=0:y=3(0)−122=−122=−6y = \frac{3(0) – 12}{2} = \frac{-12}{2} = -6y=23(0)−12=2−12=−6
Thus, one solution is (0,−6)(0, -6)(0,−6).
Solution 2:
Let x=2x = 2x=2:y=3(2)−122=6−122=−62=−3y = \frac{3(2) – 12}{2} = \frac{6 – 12}{2} = \frac{-6}{2} = -3y=23(2)−12=26−12=2−6=−3
Thus, the second solution is (2,−3)(2, -3)(2,−3).
Solution 3:
Let x=4x = 4x=4:y=3(4)−122=12−122=02=0y = \frac{3(4) – 12}{2} = \frac{12 – 12}{2} = \frac{0}{2} = 0y=23(4)−12=212−12=20=0
Thus, the third solution is (4,0)(4, 0)(4,0).
Summary of solutions:
The three ordered pairs that satisfy the equation 3x−2y=123x – 2y = 123x−2y=12 are:
- (0,−6)(0, -6)(0,−6)
- (2,−3)(2, -3)(2,−3)
- (4,0)(4, 0)(4,0)
Explanation:
For each solution, we substituted a value of xxx into the equation and then calculated the corresponding value of yyy. The equation represents a linear relationship between xxx and yyy, and for any given value of xxx, we can find a corresponding yyy. These points lie on the line represented by the equation 3x−2y=123x – 2y = 123x−2y=12.
