Question

B is the midpoint of AC. If AB = 3x + 7y and BC = 5x + 4y, solve for y in terms of x.

a. y = (3x - BC + 7y)/4
b. y = (3x + BC - 7y)/4
c. y = (BC - 3x + 7y)/4
d. y = (BC + 3x - 7y)/4

Answer 1

To solve for y in terms of x, the equation 3x + 7y = 5x + 4y can be rearranged by subtracting 4y from both sides and subtracting 3x from both sides. The solution is y = (2/3)x.

Step-by-step explanation:

To solve for y in terms of x, we need to set up an equation using the given information. Since B is the midpoint of AC, AB and BC are equal in length. We can set up the equation: AB = BC. Substituting the given values, we get 3x + 7y = 5x + 4y. To isolate y, we can subtract 4y from both sides and subtract 3x from both sides, resulting in 3y = 2x. Finally, dividing both sides by 3 gives us the solution: y = (2/3)x.