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 are the solutions to the systems of equations using the elimination method. 1) Given the system of equations: 2x + y = 6 &(1) \\ 2x - y = 2 &(2) Step 1: Add equation (1) and equation (2) to eliminate y. (2x + y) + (2x - y) = 6 + 2 4x = 8 Step 2: Solve for x. x = (8)/(4) x = 2 Step 3: Substitute the value of x into equation (1) to find y. 2(2) + y = 6 4 + y = 6 y = 6 - 4 y = 2 The solution is x=2, y=2. 2) Given the system of equations: 2x - y = 2 &(1) \\ 2x - 5y = -6 &(2) Step 1: Subtract equation (2) from equation (1) to eliminate x. (2x - y) - (2x - 5y) = 2 - (-6) 2x - y - 2x + 5y = 2 + 6 4y = 8 Step 2: Solve for y. y = (8)/(4) y = 2 Step 3: Substitute the value of y into equation (1) to find x. 2x - (2) = 2 2x - 2 = 2 2x = 2 + 2 2x = 4 x = (4)/(2) x = 2 The solution is x=2, y=2. 3) Given the system of equations (interpreting x+4y-14 as x+4y=14): x + 4y = 14 &(1) \\ -2x + y = 10 &(2) Step 1: Multiply equation (1) by 2 to make the coefficients of x opposites. 2(x + 4y) = 2(14) 2x + 8y = 28 &(3) Step 2: Add equation (3) and equation (2) to eliminate x. (2x + 8y) + (-2x + y) = 28 + 10 9y = 38 Step 3: Solve for y. y = (38)/(9) Step 4: Substitute the value of y into equation (2) to find x. -2x + (38)/(9) = 10 -2x = 10 - (38)/(9) -2x = (90)/(9) - (38)/(9) -2x = (52)/(9) x = (52)/(9) × (-(1)/(2)) x = -(26)/(9) The solution is x=-(26)/(9), y=(38)/(9). Send me the next one 📸