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
Step 1: Write down the given system of linear equations. 3x - 4y = 5 (1) 9x + y = 4 (2) Step 2: Use the elimination method. Multiply equation (2) by 4 to make the coefficients of y opposites. 4 × (9x + y) = 4 × 4 36x + 4y = 16 (3) Step 3: Add equation (1) and equation (3). (3x - 4y) + (36x + 4y) = 5 + 16 3x + 36x - 4y + 4y = 21 39x = 21 Step 4: Solve for x. x = (21)/(39) x = (7)/(13) Step 5: Substitute the value of x into equation (2) to solve for y. 9x + y = 4 9((7)/(13)) + y = 4 (63)/(13) + y = 4 Step 6: Isolate y. y = 4 - (63)/(13) y = (4 × 13)/(13) - (63)/(13) y = (52)/(13) - (63)/(13) y = (52 - 63)/(13) y = -(11)/(13) The solution to the system of equations is x = (7)/(13) and y = -(11)/(13). The solution set is \((7)/(13), -(11)/(13))\. What's next?