This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
ScanSolve AI Answer
Here are the solutions for the remaining parts of Question 5: B) Step 1: Rearrange the equation to isolate the y term. Subtract x and 4 from both sides. x - 3y + 4 = (2)/(3)x - 1 -3y = (2)/(3)x - x - 1 - 4 -3y = ((2)/(3) - (3)/(3))x - 5 -3y = -(1)/(3)x - 5 Step 2: Divide both sides by -3 to solve for y. y = (-1)/(3)x-3 - (5)/(-3) y = (1)/(9)x + (5)/(3) Step 3: Compare the equation to the standard form of a linear function, y = mx + c. The equation y = (1)/(9)x + (5)/(3) is in the form y = mx + c, where m = (1)/(9) and c = (5)/(3). Therefore, it is a linear function. Yes, it is a linear function. C) Step 1: Eliminate the denominators by multiplying both sides by 2x. (x-y)/(2x) = (2x-3y)/(2) 2(x-y) = 2x(2x-3y) x-y = x(2x-3y) Step 2: Expand the right side of the equation. x-y = 2x^2 - 3xy Step 3: Attempt to isolate y. -y + 3xy = 2x^2 - x y(-1 + 3x) = 2x^2 - x y = (2x^2 - x)/(3x - 1) Step 4: Compare the equation to the standard form of a linear function, y = mx + c. The equation contains x^2 and x in the denominator, which means it cannot be written in the form y = mx + c. Therefore, it is not a linear function. No, it is not a linear function. D) Step 1: Simplify the left side of the equation. Assuming x-y ≠ 0, the fraction (x-y)/(x-y) simplifies to 1. (x-y)/(x-y) = x + y 1 = x + y Step 2: Isolate y by subtracting x from both sides. y = -x + 1 Step 3: Compare the equation to the standard form of a linear function, y = mx + c. The equation y = -x + 1 is in the form y = mx + c, where m = -1 and c = 1. Therefore, it is a linear function (with the condition x ≠ y). Yes, it is a linear function. E) Step 1: Eliminate the denominators by multiplying both sides by the least common multiple of 3 and 2, which is 6. (2x+2y)/(3) = (3(x+2y))/(2) 6 · (2x+2y)/(3) = 6 · (3(x+2y))/(2) 2(2x+2y) = 3 · 3(x+2y) 4x+4y = 9(x+2y) Step 2: Expand the right side of the equation. 4x+4y = 9x+18y Step 3: Collect y terms on one side and x terms on the other side. 4y - 18y = 9x - 4x -14y = 5x Step 4: Solve for y by dividing both sides by -14. y = -(5)/(14)x Step 5: Compare the equation to the standard form of a linear function, y = mx + c. The equation y = -(5)/(14)x is in the form y = mx + c, where m = -(5)/(14) and c = 0. Therefore, it is a linear function. Yes, it is a linear function. 3 done, 2 left today. You're making progress.