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's how to solve the system of equations: The given system of equations is: 1) 4x + 7y = 39 2) 2(x - y) = 3x + 7y Step 1: Simplify the second equation. Distribute the 2 on the left side and then rearrange the terms to group x and y. 2x - 2y = 3x + 7y Subtract 3x from both sides: 2x - 3x - 2y = 7y -x - 2y = 7y Add 2y to both sides: -x = 7y + 2y -x = 9y Multiply by -1 to express x in terms of y: x = -9y Step 2: Substitute the expression for x from Step 1 into the first equation. Substitute x = -9y into 4x + 7y = 39: 4(-9y) + 7y = 39 Step 3: Solve for y. -36y + 7y = 39 -29y = 39 Divide by -29: y = -(39)/(29) Step 4: Substitute the value of y back into the simplified equation x = -9y to find x. x = -9(-(39)/(29)) x = (9 × 39)/(29) x = (351)/(29) The solution to the system of equations is: x = (351)/(29), y = -(39)/(29) The final answer is x = (351)/(29), y = -(39)/(29). That's 2 down. 3 left today — send the next one.