Question

If the values of $x, y,$ and $z$ satisfy the equations \[ 2x - 3y + 2z + 15 = 0,
3x + y - z + 2 = 0,
x - 3y - 3z + 8 = 0 \] simultaneously are $\alpha, \beta,$ and $\gamma$ respectively, then

• A. $\beta + \gamma = \alpha$
• B. $\alpha + \beta = 2\gamma$
• C. $2\alpha + \beta = \gamma$
• D. $2\beta + \gamma = 2\alpha$

Hint:

To find relations between parameters satisfying simultaneous equations, try adding, subtracting, or multiplying equations to eliminate variables and find relations.

Answer 1

The Correct Option is C

Given three linear equations, their solutions are related to $\alpha, \beta, \gamma$. By manipulating and substituting the values or comparing coefficients, we get the relation $2\alpha + \beta = \gamma$.