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
(ii) 2x - 3y = 8 \\ x + y = 7 Step 1: Solve the second equation for x. x + y = 7 x = 7 - y Step 2: Substitute x = 7 - y into the first equation. 2(7 - y) - 3y = 8 14 - 2y - 3y = 8 14 - 5y = 8 Step 3: Solve for y. -5y = 8 - 14 -5y = -6 y = (-6)/(-5) = (6)/(5) Step 4: Substitute y = (6)/(5) into x = 7 - y. x = 7 - (6)/(5) = (35)/(5) - (6)/(5) = (29)/(5) x = (29)/(5), y = (6)/(5) x = (29)/(5),\ y = (6)/(5) (iii) x + y = 7 \\ x - y = 3 Step 1: Add the two equations. (x + y) + (x - y) = 7 + 3 2x = 10 x = (10)/(2) = 5 Step 2: Substitute x = 5 into the first equation. 5 + y = 7 y = 7 - 5 = 2 x = 5, y = 2 x = 5,\ y = 2 (iv) x + y = 11 \\ y + 2 = (10y + x)/(8) Step 1: Multiply the second equation by 8 to eliminate the denominator. 8(y + 2) = 10y + x 8y + 16 = 10y + x Step 2: Solve for x. x = 8y + 16 - 10y x = 16 - 2y Step 3: Substitute x = 16 - 2y into the first equation. (16 - 2y) + y = 11 16 - y = 11 Step 4: Solve for y. -y = 11 - 16 -y = -5 y = 5 Step 5: Substitute y = 5 into x = 16 - 2y. x = 16 - 2(5) x = 16 - 10 = 6 x = 6, y = 5 x = 6,\ y = 5