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
To solve the system of equations: 1) 4x + 3y = 14 2) 2x - 2y = 2 We will use the elimination method. Step 1: Multiply the second equation by 2 to make the coefficients of x match. 2 × (2x - 2y) = 2 × 2 4x - 4y = 4 (Equation 3) Step 2: Subtract Equation 3 from Equation 1. (4x + 3y) - (4x - 4y) = 14 - 4 4x + 3y - 4x + 4y = 10 7y = 10 Step 3: Solve for y. y = (10)/(7) Step 4: Substitute the value of y into Equation 2 to solve for x. 2x - 2((10)/(7)) = 2 2x - (20)/(7) = 2 Step 5: Add (20)/(7) to both sides of the equation. 2x = 2 + (20)/(7) To add the numbers, find a common denominator for 2, which is (14)/(7). 2x = (14)/(7) + (20)/(7) 2x = (14 + 20)/(7) 2x = (34)/(7) Step 6: Divide by 2 to solve for x. x = (34)/(7) ÷ 2 x = (34)/(7) × (1)/(2) x = (34)/(14) Simplify the fraction by dividing the numerator and denominator by 2. x = (17)/(7) The solution to the system of equations is: x = (17)/(7) y = (10)/(7)