This English question involves literary analysis, grammar, or writing skills. The detailed response below provides a well-structured answer with supporting evidence and clear explanations.
ScanSolve AI Answer
Step 1: Check for consistency of the equations. The given equations are: 1) x + 3y = 6 2) 2x - 3y = 12 Comparing these equations with the standard form a_1x + b_1y + c_1 = 0 and a_2x + b_2y + c_2 = 0, we get the coefficients: For equation (1): a_1 = 1, b_1 = 3, c_1 = -6 For equation (2): a_2 = 2, b_2 = -3, c_2 = -12 Now, find the ratios of the coefficients: (a_1)/(a_2) = (1)/(2) (b_1)/(b_2) = (3)/(-3) = -1 (c_1)/(c_2) = (-6)/(-12) = (1)/(2) Since (a_1)/(a_2) ≠ (b_1)/(b_2) (as (1)/(2) ≠ -1), the lines intersect at a unique point. Therefore, the pair of equations is consistent. Step 2: Find points for equation (1). For the equation x + 3y = 6, we find a few points: • If x = 0, then 3y = 6 y = 2. Point: (0, 2) • If y = 0, then x = 6. Point: (6, 0) • If x = 3, then 3 + 3y = 6 3y = 3 y = 1. Point: (3, 1) Step 3: Find points for equation (2). For the equation 2x - 3y = 12, we find a few points: • If x = 0, then -3y = 12 y = -4. Point: (0, -4) • If y = 0, then 2x = 12 x = 6. Point: (6, 0) • If x = 3, then 2(3) - 3y = 12 6 - 3y = 12 -3y = 6 y = -2. Point: (3, -2) Step 4: Determine the solution graphically. When you plot these points on a graph and draw the lines, you will observe that both lines intersect at the point (6, 0). This is the unique solution to the pair of equations. Thus, the solution is: x = 6, y = 0 x = 6, y = 0 That's 2 down. 3 left today — send the next one.