Multiple choice

Find the values of x, y and z that solve the given set of equations. 2x + 5y - z = 27, x + y + z = 6 and 2y + 5z = -4

  1. x = 5, y = 2, z = 3

  2. x = 5, y = 3, z = - 2

  3. x = 5, y = - 3, z = 2

  4. x = 3, y = 2, z = 5
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Solving the system: 1) 2x + 5y - z = 27, 2) x + y + z = 6, 3) 2y + 5z = -4. From (2), z = 6 - x - y. Substitute into (1) and (3) to solve for x and y. Testing option B: 2(5) + 5(3) - (-2) = 10 + 15 + 2 = 27 (Correct). 5 + 3 + (-2) = 6 (Correct). 2(3) + 5(-2) = 6 - 10 = -4 (Correct).

AI explanation

Add the first two equations to eliminate z, yielding 3x + 6y = 33, which simplifies to x + 2y = 11. Substitute x from the second equation as x = 6 - y - z into this new equation to get 6 + y - z = 11. Substitute the third equation into this result to find y = 3. Placing y = 3 into the equations gives z = -2 and x = 5, confirming the values are x = 5, y = 3 and z = -2.

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