Final Answer:
3x+2y=3 by -2 the equivalent equation is -6x-4y = 9.
Step-by-step explanation:
To find the equivalent equation of 3x + 2y = 3 by -2, we follow these steps:
1. Isolate the variable x on one side of the equation. To do this, we subtract 2 times the coefficient of y (which is 2) from both sides of the equation and then divide both sides by the coefficient of x (which is 3). This gives us:
x = (-2/3)y - 1/3
2. Now, we want to isolate y on one side of the equation. To do this, we divide both sides of the equation in step 1 by (-2/3), which gives us:
y = (-3/2)x + (3/2)
3. Finally, we interchange x and y to get the equivalent equation with y on the left-hand side. This gives us:
-6x - 4y = 9
In this equivalent equation, we can see that x and y are related by a linear function with a slope of -6 and a y-intercept of 9. This means that as x decreases by one unit, y decreases by six units, and when x is zero, y is equal to 9.