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 find the expression with the largest value, we first need to solve the given system of linear equations for x, y, and z. The system of equations is: 1. 2x - y = 4 2. 2x + 3z = 14 3. 2y - z + 8 = 0 2y - z = -8 Step 1: Express y in terms of x from equation (1). From 2x - y = 4, we get y = 2x - 4. (Equation 1a) Step 2: Express z in terms of y from equation (3). From 2y - z = -8, we get z = 2y + 8. (Equation 3a) Step 3: Substitute Equation 1a into Equation 3a to express z in terms of x. z = 2(2x - 4) + 8 z = 4x - 8 + 8 z = 4x (Equation 3b) Step 4: Substitute Equation 3b into equation (2) to solve for x. 2x + 3(4x) = 14 2x + 12x = 14 14x = 14 x = 1 Step 5: Substitute the value of x back into Equation 1a and Equation 3b to find y and z. For y: y = 2(1) - 4 y = 2 - 4 y = -2 For z: z = 4(1) z = 4 So, the solution to the system is x=1, y=-2, z=4. Step 6: Evaluate each given expression using x=1, y=-2, and z=4. A. x + 2y = 1 + 2(-2) = 1 - 4 = -3 B. 2y + z = 2(-2) + 4 = -4 + 4 = 0 C. 2x - 3z = 2(1) - 3(4) = 2 - 12 = -10 D. 3y + z = 3(-2) + 4 = -6 + 4 = -2 E. 3x - z = 3(1) - 4 = 3 - 4 = -1 Step 7: Compare the values to find the largest one. The values are -3, 0, -10, -2, and -1. The largest value among these is 0. The expression with the largest value is 2y + z. The final answer is B. 2y + z. 3 done, 2 left today. You're making progress.